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Strengthening of RC Beams Using Externally Bonded Fibre Reinforced Polymer Composites
Structures 14 (2018) 137–152
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Strengthening of RC Beams Using Externally Bonded Fibre Reinforced Polymer Composites
T
⁎
A.N. Nayaka, , A. Kumaria, R.B. Swainb a b
Department of Civil Engineering, Veer Surendra Sai University of Technology, Burla, 768018 Sambalpur, Odisha, India Sambalpur University, Burla, Sambalpur, Odisha, India
A R T I C LE I N FO
A B S T R A C T
Keywords: Design proposals Failure modes Flexural strengthening GFRP fabrics RC beams
An experimental study is presented on the behaviour of reinforced concrete (RC) beams retrofitted externally with glass fibre reinforced polymer (GFRP) fabrics. Out of ten beams, one beam without GFRP and nine beams wrapped in various lay-up patterns with one, two, three and four layers of GFRP fabrics have been tested for flexure under two-point loading. Loads corresponding to the first crack/delamination and ultimate failure of the beams have been recorded and types of failure have also been observed. Load versus deflection graphs have been plotted at salient locations of beams. Thereafter, a critical discussion has been made with respect to increase in the flexural strength of retrofitted beams as compared to the control beam in order to explore the optimal use of GFRP fabrics for strengthening the RC beams. In addition, a design proposal has been developed in extension to IS: 456-2000 to predict the ultimate design strength of RC beams strengthened with fibre reinforced polymer (FRP) fabric sheets. Thereafter, the values of the experimental flexural strength of the strengthened RC beam have been compared with the corresponding values of design flexural strength computed from present formulation and ACI: 440-2R-08 for its validation. The results obtained from the present experimental study show that flexural strength of the strengthened RC beams increases with increase in number of layers for all lay-up patterns. However, the beams wrapped with two layers GFRP fabrics in the tension face and half of the both sides below neutral axis show superior performance with respect to flexural strength, ductility and economy.
1. Introduction The major problem faced by civil engineers worldwide is a premature deterioration in concrete structures. FRP fabrics/laminates have been introduced as the advanced materials for strengthening/retrofitting of existing concrete structures since more than two decades due to their high strength, low weight, corrosion resistance, high fatigue resistance, easy and rapid installation and minimal change in structural geometry. A lot of research works have been done and some field applications have also been conducted on the strengthening of RC beams/ girders using externally bonded FRP laminates/sheets. Several investigators [1–12] carried out experimental investigations on RC beams/girders retrofitted with Carbon/Glass/Aramid fibre reinforced polymer (CFRP/GFRP/AFRP) composites in order to study their efficacy. Most of the experimental works were carried out on CFRP fabrics/ sheets/laminates in strengthening of RC structures which showed that the strengthening with externally wrapped CFRP laminates/sheets in the tension face significantly increased the strength in bending, reduced the deflections as well as crack width of the RC beams in comparison to
⁎
other types of FRPs [13–27]. There are also some notable studies related to the application of externally wrapped GFRP composites for strengthening the RC beams, which showed that U wrapping of GFRP sheet is an effective way to enhance the flexural capacity of RC beams [28–37]. However, most often the strengthened beams with FRP composite failed in a brittle way, mainly due to the loss of contact between the composite material and the concrete [38–40]. Further, various theoretical calculations and numerical simulations were also proposed by various researchers [14,41–47] in order to estimate the ultimate load carrying capacity, flexural strength and ductility of FRP strengthened RC beams and found to be in good agreement with the experimental results. In addition to the above research works, several design guidelines [48–52] in various countries have been brought forth in these days for strengthening/retrofitting of concrete structures using externally wrapped FRP sheets. All the above design guidelines are based on the traditional sectional analysis called “plane sections before bending remain plane after bending”. However, there is discrepancy in the design results due to differences in adopting safety factors. Moreover,
Corresponding author. E-mail address: [email protected] (A.N. Nayak).
https://doi.org/10.1016/j.istruc.2018.03.004 Received 8 December 2017; Received in revised form 4 March 2018; Accepted 6 March 2018 Available online 07 March 2018 2352-0124/ © 2018 Institution of Structural Engineers. Published by Elsevier Ltd. All rights reserved.
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topographical and ecological conditions as well as social background are different in each country and the prerequisites for design of RC structures using externally bonded FRP laminates may not be same. Therefore, a thorough experimental investigation is required in a country to upgrade its design guidelines time to time so that the discrepancy between the experimental results and the results obtained from the design guidelines will reduce. Therefore, the present investigation aims to study the behaviour of the flexural strengthening of RC beams using externally bonded GFRP fabrics. The study includes the effects of different parameters such as number of layers and wrapping scheme/patterns of GFRP fabric on strength, deflection and ductility of RC beams. In addition to the above experimental work, a theoretical model for flexural strengthening is also developed with the extension of IS: 456-2000 [53]. The ultimate flexural strength obtained from the experimental investigation is also compared with those predicted from the proposed design proposal and ACI: 440-2R-08 [40].
Percentage passing
100 80 60 40
Min IS:383 [61] (Zone-III) Max IS:383 [61] (Zone-III)
20
Fine Aggregate
0 0.15
0.3
0.6 1.18 Sieve size (mm)
2.36
4.75
Fig. 1. Grading analysis of fine aggregate.
2. Experimental investigation
120
In order to study the structural performance of RC beams strengthened with GFRP fabrics, ten beams were prepared, out of which one without GFRP fabric and the remaining nine beams wrapped with GFRP fabrics. All the RC beams were tested under two-point loading. Accordingly, characterization of materials such as cement, aggregates, steel and GFRP fabric, preparation of specimen, wrapping of GRFP fabrics on beams, testing and observations are presented and discussed in the following sub-sections.
Percentage passing
100
2.1. Testing of materials
80 60 Min-IS: 383 [61]for 20mm nominal size Max-IS: 383 [61] for 20mm nominal size Coarse Aggregate
40 20
2.1.1. Cement Fresh Ultratech Portland Slag Cement (PSC) conforming to IS: 4551989 [54] was used for the preparation of all beam specimens. The required physical and mechanical properties of cement were determined in accordance to Indian standard specifications [55–59]. The test results of physical and mechanical properties of cement along with the standard test methods are presented in Table 1. It is found that the above cement satisfies the specification of PSC as per IS: 455-1989 [54].
0 4.75
10 20 Sieve size(mm)
40
Fig. 2. Grading analysis of 20 mm coarse aggregate.
the requirements in accordance to IS: 383-1970 [61]. From Figs. 1 and 2, it is observed that the grading of fine aggregate and 20 mm coarse aggregate are satisfying the grading limits in accordance to IS: 3831970 [61]. Further, other physical and mechanical properties such as bulk density, specific gravity, water absorption, impact value, abrasion value and crushing value were obtained as per IS: 2386-1963 (part 3 and part 4) [62,63] and the results of the same are furnished in Table 2 along with test methods. From this table, it is seen that these properties are within the limit specified by IS-383-1970 [61].
2.1.2. Aggregates Sand collected from local river was used as fine aggregate. The Crushed granite of 20 mm nominal size was used as coarse aggregates for preparing concrete. The sieve analysis of fine aggregate and coarse aggregate were carried out as per IS: 2386-1963 (Part 1) [60] and the results of the same are shown in Figs. 1 and 2, respectively along with Table 1 Physical and mechanical properties of cement. Properties
Test method
Test results
IS:455 limit [54]
Fineness (cm2/g)
IS 4031: 1988 (part-2) [56] IS 4031: 1988 (part-11) [55] IS 4031: 1988 (part-4) [57] IS 4031: 1988 (part-5) [58]
3300 3.14
Not less than 2250 –
32
–
105 535
Not less than 30 Not more than 600
Specific gravity Standard consistency (%) Setting time (min) Initial setting time (min) Final setting time (min) Compressive strength (MPa) 3 days 7 days 28 days
2.1.3. Steel High yield strength deformed (HYSD) bars of Fe415 grade were used as the reinforcement for the preparation of RC beam specimens. The mechanical properties of the reinforcing steel bar were obtained through tensile strength test in the Universal Testing Machine (UTM) confirming to IS: 1786-2008 [64]. The stress-strain curve obtained from the tensile strength test of HYSD bar of 8 mm diameter is shown in Fig. 3. From the tensile strength test, the average yield strength, ultimate strength and percentage elongation of HYSD bars were obtained as 428.6 MPa, 506.6 MPa and 21.7, respectively. 2.1.4. GFRP fabrics A GFRP fabric used in the present study is a fabric of 0.275 mm thick and is made up of stitching cross glass fibres. Four coupons were prepared by binding four layers of GFRP fabrics with binding materials Epoxy and Hardener in the ratio of 9:1. The top view, side view and
IS 4031: 1988 (part-6) [59] 16.87 22.33 36.26
Not less than 16 Not less than 22 Not less than 33
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Table 2 Physical and mechanical properties of aggregates. Properties
Test method
Specific gravity Water absorption (%) Free surface moisture (%) Loose bulk density (kg/m3) Compact bulk density (kg/m3) Impact value (%) Abrasion value (%) Crushing value (%)
IS: IS: IS: IS: IS: IS: IS: IS:
2386 2386 2386 2386 2386 2386 2386 2386
(part-3) (part-3) (part-3) (part-3) (part-3) (part-4) (part-4) (part-4)
[62] [62] [62] [62] [62] [63] [63] [63]
Fine aggregate
Coarse aggregate
IS: 383 limit [61]
2.6 1.0 Nil 1443 1566 – – –
2.8 0.5 0.38 1448 1615 22.42 25.23 20.39
– – – – – 45 50 45
displacement at peak load, displacement at breaking load, stress at peak, strain at peak, stress at 0.2% yield, strain at 0.2% yield and Young's modulus. The above results are presented in Table 3. Average ultimate strength and ultimate elongation of the GFRP fabric are 236.5 MPa and 4.084%, respectively. It is worth mentioning that the elongation at the peak load is 4.069%, which is slightly less than the ultimate elongation. It indicates the brittle failure of GFRP.
500
Stress (Mpa)
400
300
2.2. Preparation of specimen
200
Concrete mix design was done for M25 grade concrete according to IS: 10262-2009 [66]. All the RC beam specimens of size 120 mm × 150 mm × 1000 mm were prepared with M25 grade concrete and Fe415 grade steel. Three concrete cubes of size 150 mm were prepared along with the preparation of each beam specimen. The beams and cubes were allowed for 28 days curing in water at 27 ± 2 °C temperature. The beam with dimensions and reinforcement details is presented in Fig. 5.
100
0 0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
Strain Fig. 3. Stress-strain curve of HYSD bar.
2.3. Wrapping of GFRP fabrics
photograph of the prepared coupons along with its dimension are presented in Fig. 4(a), (b) and (c) respectively. All the coupons were tested in the INSTRON machine as per ASTM D7565-10-2017 [65] in order to obtain its properties like peak load, breaking load,
150mm
50mm 25 mm
50mm
In order to fulfil the objective, ten RC beams were tested with twopoint loading. Out of which, nine RC beams were wrapped with GFRP fabrics in different layers and lay-up patterns and one RC beam was
(a) Top View Gauge length 4 layers of GFRP fabrics Aluminium Plate (b) Side View
(c) photograph of GFRP coupon Fig. 4. Details of GFRP coupon.
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Table 3 Test results of GFRP coupons. Sp.no.
Peak load (kN)
Breaking load (kN)
Displacement at peak (mm)
Displacement at break (mm)
Stress at peak (MPa)
Strain at peak (%)
Stress at 0.2% yield (MPa)
Strain at 0.2% yield (%)
Young's modulus (MPa)
1 2 3 4 Mean
7.784 6.157 7.644 7.535 7.280
7.784 6.804 7.644 7.535 7.442
6.251 5.942 6.080 6.138 6.103
6.251 6.034 6.080 6.138 6.126
254.2 203.8 248.8 239.2 236.5
4.168 3.961 4.054 4.092 4.069
104.90 86.22 112.90 101.70 101.40
1.270 1.095 1.318 1.239 1.231
9714 9675 9583 9928 9825
load/delamination load. Then the load was applied up to the failure of the beam. The deflections corresponding to the respective loads at three salient points i.e. L/3, L/2 & 2L/3 of the beams were recorded by fixing three dial gauges at these locations from the left support, where L is the centre to centre distance between both the supports. During the testing it was observed that all the ten beams showed almost similar behaviour in the initial stage of loading. In case of the beam BT00, the first hair crack occurred at the first load point (L/3) at a load of 38.0 kN. Thereafter, the longitudinal reinforcement started yielding with increase in load due to which the crack got widened. Finally, flexural failure occurred due to complete yielding of the longitudinal reinforcement and then crushing of concrete in compression zone at a load of 48.0 kN as expected. The above failure is shown in Fig. 10. In the beam BT11 (1 layer GFRP at bottom and 25 mm on both sides), the first crack appeared at a load of 46.3 kN with partial rupture of fibre at the middle third of the bottom portion due to the yielding of longitudinal reinforcement. With further increase in load, the beam finally failed due to complete yielding of longitudinal reinforcement and rupture of GFRP fabric at the bottom and thereby crushing of concrete at the top at a load of 50.7 kN indicating flexural failure (Fig. 11). The beam BT12 (2 layers of GFRP at the bottom and 25 mm on both sides) showed almost similar behaviour as in case of BT11. When the load gradually increased, the longitudinal reinforcement started yielding due to which the tearing of GFRP started at the bottom part and side vertical cracks initiated from the tearing of GFRP in the flexural zone at a load of 61.8 kN. Then, the yielding of longitudinal reinforcement went on with increase in load due to which the tearing of GFRP increased and side vertical cracks got widened. Finally, the
kept without GFRP fabric for reference. Before wrapping with GFRP fabrics in wet lay-up system, a standard procedure was followed to ensure a well prepared concrete surface for proper bonding between concrete and GFRP fabric. The binding material was brushed on the prepared concrete surface. Then, wrapping of GFRP was done layerwise and pressed with a roller to remove air void. The beam without GFRP fabric was designated as BT00. From the remaining nine beams wrapped with GFRP fabrics, four beams were wrapped fully with GFRP fabrics at the bottom portion and 25 mm height at both sides from the bottom in one, two, three and four layers and were designated as BT11, BT12, BT13 and BT14, respectively. Similarly, another four beams were wrapped fully with GFRP fabrics at the bottom portion and lower half (75 mm) of both sides in one, two, three and four layers and were designated as BT21, BT22, BT23 and BT24, respectively. For the remaining one beam, the bottom and two sides were wrapped completely with one layer of GFRP, which was designated as BT31. A typical wrapping of the beams with GFRP fabric is shown in Fig. 6(a) and (b). The detail wrapping scheme of GFRP fabrics with different layers are shown in Fig. 7. Finally, the specimens were kept for 7 days air curing at a temperature of 27 ± 2 °C before the testing.
2.4. Testing and observation The beam specimens were tested in the Universal Testing Machine (UTM-1000 kN) under two-point loading. The schematic diagram of experimental test set up is shown in Fig. 8 and the photograph of experimental test set up in UTM is shown in Fig. 9. The load at which the first visible crack/delamination appeared was recorded as the cracking
150 mm
120 mm
4-8 mmØ
(a) Cross Section 1000 mm
2- legged 8mm dia. vertical Stirrups @200mm c/c (b) Longitudinal Section Fig. 5. Dimensions and reinforcement details of RC beams.
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(a) GFRP Fabrics
(b) Beam surface. Fig. 6. Wrapping of beam with GFRP fabric.
flexural failure occurred due to complete yielding of longitudinal reinforcement and tearing of GFRP and then crushing of concrete in compression zone at a load of 68.8 kN (Fig. 12). In BT13 (3 layers of GFRP at the bottom and 25 mm on both sides), first crack developed at a load of 67.2 kN and then the tearing of GFRP at mid-span of the bottom portion started at a load of 70.0 kN. The failure of the beam was observed at a load of 96.0 kN with the development of wide vertical crack extending from the bottom to top at mid-span and complete debonding of GFRP fabrics from concrete in the middle third portion without crushing of concrete at the top indicating shear failure (Fig. 13). In BT14 (4 layers of GFRP at the bottom portion and 25 mm on both sides), diagonal shear crack initiated from the top portion of the beam near left load point at a load of 85.0 kN. With increase in load, the crack got widened and moved making an angle of about 45° with the beam axis towards the left support up to level of the retrofitting portion (25 mm from bottom) and moved horizontally towards left end of beam. Finally, the failure occurred at a load of 109.5 kN due to the debonding of GFRP fabrics from concrete surface indicating shear failure (Fig. 14). In BT21 (1 layer of GFRP at the bottom and 75 mm on both sides), the first crack developed at 63.5 kN at mid-span. With increase in load, the longitudinal reinforcement started yielding due to which the tearing of GFRP sheet was observed in the tension face in the flexural zone and the crack got widened. Finally, the flexural failure of the beam occurred
due to complete yielding of longitudinal reinforcement and tearing of GFRP fabrics in the tension face and subsequent crushing of concrete in the compression face at a load of 77.4 kN (Fig. 15). The beam BT22 showed the similar behaviour as the beams BT11, BT12 and BT21. With gradual increase in load, the longitudinal reinforcement started yielding which initiated the tearing of GFRP sheet and vertical crack in the flexural zone at a load of 80.0 kN. Finally the failure occurred due to complete yielding of the longitudinal reinforcement and tearing of GFRP sheet in the tension face and subsequent crushing of concrete in the compression face in the flexural zone at a load of 95.4 kN indicating flexural failure (Fig. 16). In BT23 (3 layers of GFRP at the bottom and 75 mm on both sides) the debonding of GFRP fabrics started at 60.0 kN and two inclined cracks initiated from the top of the beam at L/3 and 2L/3 load points at load of 70.0 kN. With an increase in load, both the cracks got widened and moved downward diagonally towards both the supports. Finally, the beam failed due to the combined effects of the widening of both cracks and tearing of GFRP fabrics in the bottom portion and crushing of concrete in compression face of mid-span at a load of 115.2 kN indicating flexure-shear failure (Fig. 17). In BT24 (4 layers of GFRP at the bottom and 75 mm on both sides) the first crack appeared at the loading point of L/3 at a load of 81.8 kN and propagated downward diagonally towards the left support with further increase in load. Thereafter, the debonding of GFRP fabrics started at 105.0 kN. Finally, complete separation of GFRP sheets from the beam 141
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8 mmØ @90mm c/c
25 mm 1 layer GFRP
8 mmØ @90mm c/c
8 mmØ @90mm c/c
1 layer GFRP
3 layer GFRP
(g) BT22
(h) BT23 120 mm
8 mmØ @90mm c/c
150 mm
150 mm
8 mmØ @90mm c/c 75 mm
2 layer GFRP
120 mm
4-8 mmØ
4-8 mmØ
75 mm
(f) BT21
(e) BT14
120 mm
4-8 mmØ
75 mm
4 layers GFRP
(d) BT13
120 mm
4-8 mmØ
25 mm
25 mm
150 mm
8 mmØ @90mm c/c
8 mmØ @90mm c/c
3 layers GFRP
(c) BT12
150 mm
4-8 mmØ
4-8 mmØ
8 mmØ @90mm c/c
2 layers GFRP
120 mm 150 mm
150 mm
120 mm
4-8 mmØ
25 mm
(b) BT11
(a) BT00
150 mm
4-8 mmØ
150 mm
8 mmØ @90mm c/c
150 mm
150 mm
4-8 mmØ
120 mm
120 mm
120 mm
120 mm
4-8 mmØ
8 mmØ @90mm c/c
75 mm 4 layer GFRP
1 layer GFRP
(j) BT31
(i) BT24
Fig. 7. Details of wrapping of beams with different layers and lay up patterns of GFRP.
load, the horizontal tearing of GFRP sheets at the bottom two edges and separation of bottom concrete cover with GFRP sheets from the beam near right support due to shear was observed leaving the beam as a simple RC beam at a load of 101.2 kN. Finally, the beam failed at the same load like simple RC beam due to yielding of the longitudinal reinforcement and subsequent crushing of concrete in the compression face near the load point. The failure of the beam BT31 is shown in
was observed in the left third portion. Then the beam failed in shear at a load of 140.0 kN due to development of a wide diagonal cracks and rupture of GFRP fabrics with bursting sound indicating shear failure (Fig. 18). In BT31 (bottom and both sides up to full depth wrapped with 1 layer of GFRP), the debonding of GFRP sheet started with a load of 90.0 kN near the right support of the beam. With further increase in
Load
Load
L/3
L/3
L/3
Dial gauge Fig. 8. Schematic diagram of experimental test set up.
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beyond which there is a decrease in load to 40.6 kN with increase in deflections up to 23 mm showing sufficient plasticity. In the beam BT12, the deflection increases up to 7 mm with an increase in load up to 68.0 kN. Further there is a sudden decrease in load by 11.0 kN with very little increase in deflection. Thereafter, the deflection of the beam increases up to 22 mm without further increase in load showing sufficient plasticity. On the other hand, for the beam BT13, load increases up to peak load of 96.0 kN with increase in deflection up to 14 mm and then decreases to 63.0 kN with very little increase in deflection without showing any plasticity. In case of BT14, with increase in the number of layers up to 4 layers, the load increases up to 109.0 kN (peak load) with the increase in deflection up to 15 mm. Thereafter, there is a sudden decrease in load to 73.0 kN without further increase in deflection showing brittleness. Both the beams BT13 and BT14 show the similar trend and have a brittle failure. In the beam BT21, deflection increases up to 10 mm with increase in load up to 77.0 kN, then increases up to 15 mm with gradual decrease in load up to 65.0 kN and finally increases up to 23 mm without any change in load showing sufficient ductility. With the addition of two similar layers of GFRP fabrics, the beam BT22 shows the similar trend as in the case of BT21 with the higher ultimate load, i.e. 95.0 kN. The load increases up to 95.0 kN (peak load) with the increase in deflection up to 9 mm and then gradually decreases to 60.0 kN with an increase in deflection up to 23 mm, i.e. significant increase in deflection with gradual decrease in load. Hence, the beam fails showing sufficient ductility. However, in the case of the beam BT23 the load increases up to 115.0 kN with an increase in deflection up to 13 mm and then suddenly decreases up to nearly 72.0 kN with very little increase in deflection showing brittle behaviour. Thereafter, there is very little increase in load with an increase in deflection up to 27 mm and finally, the beam fails at a load of 69.0 kN. The similar trend is observed in the case of the beam BT24, i.e. retrofitted with 4 numbers of similar layers. The load increases up to 140.0 kN with an increase in deflection up to 17 mm and then suddenly decreases to nearly 75.0 kN without any appreciable increase in deflection showing brittle behaviour. Then, deflection increases up to 28 mm with a marginal decrease in load and the beam breaks at a load of 71.0 kN. It is clearly verified during testing that the energy is released suddenly with a bursting sound in BT24. The separation of GFRP fabrics with complete debonding from the concrete surface is also observed in this case. From Figs. 20–22, it is inferred that BT24 shows more brittleness than BT23. On the other hand, in the beam retrofitted with 1 layer of GFRP fabric in all three sides (BT31), the deflections at L/3 and L/2 locations (Figs. 20–22) increases to a maximum value of 8 mm with an increase in load up to the failure point
Fig. 9. Photograph of experimental test set up in UTM.
Fig. 19. The summary of the test results of all the beams are presented in Table 4. 3. Results and discussion In order to derive a meaningful conclusion of the experimental investigation of the RC beams retrofitted with the different layers and laying patterns of GFRP fabrics, the data recorded during the testing are interpreted in different ways. At first the load versus deflection curves for all the beams at specific locations i.e. at L/3, L/2 and 2L/3 are plotted and furnished in Figs. 20–22, respectively. From Figs. 20–22, it is observed that the load versus deflection curves at the three locations have shown the similar trend. The deflections of beam BT00 at L/3, L/2 and 2L/3 locations increases up to 7 mm only with increase in load up to the failure without showing any plasticity. With addition of 1 layer of GFRP fabric retrofitted in the bottom portion and 25 mm of both sides as in case of the beam BT11, the load increases up to 50.7 kN with increase in deflection up to 12 mm
Fig. 10. Failure of beam BT00.
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Fig. 11. Failure of beam BT11.
Fig. 12. Failure of beam BT12.
fabrics before its use. Since the wrapping of the beam with GFRP in all three sides develops the brittleness in comparison to other two laying patterns keeping the number of layers constant, it is not desirable where only flexural strengthening is required. But, when the beam is required for both flexural and shear strengthening, then it may be useful for wrapping all three sides of the beam to get better strength.
(101.0 kN) showing slightly brittle behaviour due to debonding of GFRP layer. The deflection at 2L/3 increases up to 15 mm with the increase in the load having a lower slope in comparison to other two locations (Fig. 21). From the above discussion, it is clear that when the number of layers of GFRP fabrics increases in any laying pattern, the brittleness gradually increases. Similarly, wrapping the GFRP fabrics in all three sides of the beam develops the brittleness in comparison to other two laying patterns keeping the number of layers constant. In order to obtain the increase in flexural strength of the retrofitted RC beams with reference to the RC beam (BT00), the ultimate flexural strength and its percentage increase in comparison to the RC beam without GFRP fabrics are calculated from the test data and furnished in Table 5. The percentage increase is the highest for BT24 followed by BT23, BT14, BT31, BT13, BT22, BT21, BT12 and BT11. It is worth mentioning that BT22 gives nearly two times the flexural strength of RC beams with sufficient ductility with only 2 layers of GFRP wrapped in the bottom and half of both sides. Therefore, it is very much essential to ascertain the increase in ultimate strength and failure mode of any beam retrofitted with GFRP
4. Theoretical investigation In order to develop an analytical model for predicting the flexural strength of RC beams strengthened with FRP, the traditional sectional analysis is carried out in extension of IS: 456-2000 [53]. The following assumptions are made to develop the above model in addition to the assumptions considered in IS 456-2000 [53]. 1. The strain compatibility is to maintain at the interface of FRP fabrics and concrete, i.e. no slip between FRP fabrics and concrete. 2. The elastic modulus of the FRP used in the analysis shall be considered from the tensile coupon test of FRP fabrics. 144
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Fig. 13. Failure of beam BT13.
Fig. 14. Failure of beam BT14.
The above three cases are presented in the following sub-sections in order to derive the expression of design flexural strength.
An under-reinforced section of FRP strengthened RC beam is considered for the analytical investigation. The expression of design flexural strength of RC beams strengthened on the tension face of beam by wrapping FRP is normally available in various design proposals. However, in practice, in addition to the tension face, both sides of beam are wrapped partially or fully in order to strengthen the beam. Therefore, in the present study, an analysis has been made to obtain the flexural strength of the retrofitted beams for three cases as follows:
4.1. Case-I: wrapping of FRP at the tension face of the RC beam The cross-section of RC beam strengthened with FRP at the tension face of the beam, strain diagram and stress diagram for Case-I are shown in Fig. 23. From Fig. 23, the following relations can be obtained.
• Wrapping of FRP at the bottom face of the beam, i.e. in the tension face (Case-I) • Wrapping of FRP on both sides up to the section below the neutral •
axis and at the bottom face of the beam, i.e. in the tension zone (Case-II) Wrapping of FRP at the bottom part and two sides up to the depth above neutral axis i.e. in both the tension and compression zone (Case-III).
0.0035 ε2 = xu (d − x u )
(1)
0.0035 ε3 = xu (d + d′ − x u )
(2)
0.0035 ε4 = xu (d + d′ + t f − x u )
(3)
Now, the fibre strain is the average of ε3 and ε4 and can be written 145
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Fig. 15. Failure of beam BT21.
where b, d, d′, tf, xu, ε1, ε2, ε3 and ε4 are defined in Fig. 23, σf is the stress in fibre, Ef is the elastic modulus of fibre, fy is the yield stress in steel, fck is the characteristic stress of concrete, Ast is the cross-sectional area of main longitudinal reinforcement and Pt is the percentage of longitudinal steel reinforcement.
as:
εf =
ε3 + ε4 2
(4)
Therefore, stress in the fibre, σf, is expressed as
σf = εf Ef
(5)
Now, the depth of the neutral axis is obtained by equating compression and total tension and the same may be written as
0.87f y pt σf t f xu = + d 0.36fck 0.36fck d
4.2. Case-II: wrapping of FRP at the tension face and both side faces below the neutral axis The cross-section of the concrete beam strengthened with FRP at the tension face and both side faces below the neutral axis, strain diagram and stress diagram for Case II are indicated in Fig. 24. From Fig. 24, the following relations are obtained.
(6)
Now, the ultimate moment of resistance for FRP strengthened concrete beams is expressed as:
Mu =
0.87f y pt bd 2 100
t tf x d′ x ⎛1 − 0.42 u ⎞ + f bd 2σf ⎛1 + + − 0.42 u ⎞ d d d 2 d d⎠ ⎝ ⎠ ⎝
ε2 =
0.0035(h − x u − hf )
(7)
Fig. 16. Failure of beam BT22.
146
xu
(8)
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A.N. Nayak et al.
Fig. 17. Failure showing tearing of GFRP of beam BT23.
Fig. 18. Failure of beam BT24.
ε3 =
0.0035(d − x u ) xu
(9)
ε4 =
0.0035(h − x u ) xu
(10)
ε5 =
Ff =
εfs = (11)
Ffs =
0.0035(2h + t f − 2x u ) 2x u
(12)
0.0035Ef (2h + t f − 2x u ) 2x u
(15)
2x u
0.0035Ef hf t f (2h + t f − 2x u − hf ) 2x u
(16)
Now, the depth of the neutral axis xu is evaluated by equating total compressive force and total tensile force and the same can be written as
Now, the stress in fibre, σf, is given by
σf =
0.0035(2h + t f − 2x u − hf )
Hence, the force on side wrapped FRP is given by
The fibre strain εf is the average of ε4 and ε5 and is expressed as
εf =
(14)
2x u
Similarly, the average strain of fibre along the side of the beam εfs is calculated by taking the average of ε2 and ε5 and given by
0.0035(h + t f − x u ) xu
0.0035Ef btf (2h + t f − 2x u )
0.87f y Ast + Ff + Ffs = 0.36fck bx u (13)
(17)
Now, the ultimate moment of resistance for FRP strengthened concrete beams may be expressed as:
Hence, the force on bottom FRP is given by 147
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Fig. 19. Failure of beam BT31.
Table 4 Summary of the test results. Beam type
28 days cube strength (MPa)
Cracking/delaminated load (kN)
Failure load (kN)
Contribution of strength from GFRP (kN)
Failure mode
BT00 BT11 BT12 BT13 BT14 BT21 BT22 BT23 BT24 BT31
30.5 30.7 30.7 30.4 33.7 33.8 31.7 32.9 32.2 30.8
38.0 46.3 61.8 67.2 85.0 63.5 80.0 70.0 81.8 90.0
48.0 50.7 68.8 96.0 109.5 77.4 95.4 115.2 140.0 101.2
– 2.7 20.8 48.0 61.5 29.4 47.4 67.2 92.0 53.2
Flexure failure Flexure failure Flexure failure Shear failure Shear failure Flexure failure Flexure failure Flexure-shear failure Shear failure Shear-flexure failure
140
100 80 60
100
40
80 60 40
20 0
BT00 BT11 BT12 BT13 BT14 BT21 BT22 BT23 BT24 BT31
120
Load (kN)
120
Load (kN)
140
BT00 BT11 BT12 BT13 BT14 BT21 BT22 BT23 BT24 BT31
20 0
5
10
15
20
25
30
35
Deflection (mm)
0 0
Fig. 20. Load vs. deflection at L/3 of all beams.
5
10
15
20
25
Deflection (mm) Fig. 21. Load vs. deflection at L/2 of all beams.
148
30
35
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160 BT00 BT11 BT12 BT13 BT14 BT21 BT22 BT23 BT24 BT31
140 120
Load (kN)
100 80 60
.
0.0035(2h + t f − 2xu )
The fibre strain is the average of ε4 and ε5 and
0.0035(2h + t f − 2x u )
εf =
(24)
2x u
Now, the stress in fibre, σf, is given by
0.0035Ef (2h + t f − 2x u )
σf =
(25)
2x u
Hence, the force on bottom FRP is given by
0 0
5
10
15
20
25
30
0.0035Ef btf (2h + t f − 2x u ) 2x u
Ffs =
0.0035Ef t f (h + t f − x u )2 (28)
xu
The effect of fibre in compression is neglected. Then the depth of the neutral axis ‘xu’ is obtained by equating total compressive force and total tensile force and the same may be written as
where h, hf, tf, xu, d, ε2, ε3, ε4 and ε5 are defined in Fig. 24, k is centroidal distance of force acting on a beam due to side fibres. Where
0.87f y Ast + Ff + Ffs = 0.36fck bx u
hf
(29)
Now, the ultimate moment of resistance for FRP strengthened concrete beams may be expressed as:
(19)
Mu = 0.87f y Ast (d − 0.42x u ) +
4.3. Case-III: wrapping of FRP at the tension face and both side faces above the neutral axis
0.0035Ef btf (2h + t f − 2x u ) 2x u
t ⎛h + f 2 ⎝
− 0.42x u⎞ ⎠ 0.0035Ef t f (h + t f − x u )2 + (h − k − 0.42x u ) xu
The cross-section of concrete beam strengthened with FRP at the tension face and both side faces above the neutral axis, strain diagram and stress diagram for Case III are indicated in Fig. 25. From Fig. 25, the following relations are obtained:
(30) where h, hf, tf, xu, d, ε2, ε3, ε4 and ε5 are defined in Fig. 25, k is the centroidal distance of force acting on a beam due to side fibre and is given by:
0.0035(x u − h + hf ) (20)
0.0035(d − x u ) xu
(27)
xu
Hence, the force on side wrapped FRP is given by
(18)
xu
0.0035(h + t f − x u )
εfs =
t ⎛h + f 2 ⎝
− 0.42x u⎞ ⎠ 0.0035Ef hf t f (2h + t f − 2x u − hf ) + (h + k − 0.42x u ) 2x u
2ε2 + ε5 × ε2 + ε5 3
(26)
2x u
Similarly, the average strain of fibre along the side of the beam is calculated by taking the average of ε2 and ε5 and given by
Fig. 22. Load vs. deflection at 2L/3 of all beams.
Mu = 0.87f y Ast (d − 0.42x u ) +
0.0035Ef btf (2h + t f − 2x u )
Ff =
35
Deflection (mm)
ε3 =
(23)
2x u
εf = 2xu can be written as
20
ε2 =
(22)
0.0035(2h + t f − 2x u )
ε5 =
40
k=
0.0035(h − x u ) xu
ε4 =
k=
(21)
h − xu 3
(31)
Table 5 Increase in flexural strength due to wrapping of GFRP fabrics. Beam type
Experimental ultimate moment of resistance (Mu) (kN-m)
% increase of Mu with reference to BT00
Remarks
BT00 BT11 BT12 BT13 BT14 BT21 BT22 BT23 BT24 BT31
8.00 8.45 11.46 16.00 18.25 12.83 15.90 19.20 23.33 16.87
0.0 5.6 43.2 100.0 128.1 61.0 98.7 140.0 191.6 110.8
Ductile failure Ductile failure Ductile failure Brittle failure Brittle failure Ductile failure Ductile failure Brittle failure Brittle failure Brittle failure
149
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Fig. 23. Stress-strain diagrams of FRP strengthened RC beam (Case-I).
5. Comparison between predicted and experimental results
where, As is the area of steel reinforcement, fs is the stress in the steel reinforcement, d is the distance between extreme compression fibre and centroid of tension reinforcement, β1 is the ratio between depth of equivalent rectangular stress block and depth of the neutral axis and ‘c’ is the distance between extreme compression fibre and neutral axis. Mnf is the contribution of the FRP reinforcement to the nominal flexural strength and is expressed as:
In order to validate the analytical model developed in the present study, values of the flexural strength predicted from the present design model for all the RC beams considered in the present study are compared with those obtained from experimental investigation and predicted from ACI:440-2R-08 [48]. Accordingly, the theoretical values of flexural strength of the ten RC beam considered in the experimental investigation are obtained from the present design model using Eqs. (7), (18) and (30). Similarly, the flexural strength of all above beams has been predicted from ACI: 440-2R-08 48 using the following equations.
ϕMn = ϕ ⌊Mns + φf Mnf ⌋
βc Mnf = Af f fe ⎛df − 1 ⎞ 2 ⎠ ⎝ ⎜
⎜
(34)
where, Af is the area of FRP, ffe is the effective stress in the FRP and df is the effective depth of FRP flexural reinforcement. Finally, the values of the flexural strength obtained from the experimental investigation and predicted from the present design proposal and ACI: 440-2R-08 48 for all the RC beams considered are presented in Table 6. From Table 6 it is found that, the ultimate flexural strength values of the strengthened RC beams predicted from present design proposal are in good agreement with those predicted from ACI:440-2R-08 48. But, the experimental values of the ultimate flexural strength of the strengthened beams are higher than those predicted
(32)
where, Mn is the nominal flexural strength, ϕ is the strength reduction factor for structural concrete equal to 0.90, φf is the strength reduction factor of FRP equal to 0.85 for flexure, Mns is the contribution of RC beam to the nominal flexural strength, which is expressed as:
βc Mns = As fs ⎛d − 1 ⎞ 2 ⎠ ⎝
⎟
⎟
(33)
Fig. 24. Stress-strain diagrams of FRP strengthened RC beam (Case-II).
150
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Fig. 25. Stress-strain diagrams of FRP strengthened RC beam (Case-III).
half of both sides (approximately tension zone) are wrapped with GFRP completely, shows better performance with respect to strength and ductility as compared to other two patterns, i.e. bottom portion and 25 mm of both sides, and bottom and full depth of both sides wrapped with GFRP. 3. The beams wrapped with 2 layers GFRP sheets in the tension zone of the beam (bottom portion and half of both sides) shows superior performance with respect to increase in flexural strength, failure pattern and economy in comparison to other retrofitted beams. 4. The ultimate flexural strength values of the strengthened RC beams predicted from the present model are in good agreement with those predicted from ACI: 440-2R-08 48 and lower than those obtained from experimental investigation, which needs further refinement of the present model.
Table 6 Comparison between theoretical and experimental results of flexural strength of strengthened RC beam. Beam type
BT BT BT BT BT BT BT BT BT BT
00 11 12 13 14 21 22 23 24 31
Experimental ultimate moment of resistance (Muex) (kN m)
8.00 8.45 11.46 16.00 18.25 12.83 15.90 19.20 23.33 16.87
Theoretical ultimate moment of resistance (Mu) ACI.2R.08 (Mu1)
Present method (Mu2)
4.68 5.20 5.58 5.97 6.31 – – – – –
4.562 5.04 5.404 5.704 5.98 5.01 5.593 5.936 6.208 5.244
Mu1 Muex
Mu2 Muex
0.58 0.62 0.49 0.37 0.34 – – – – –
0.57 0.59 0.47 0.35 0.32 0.39 0.35 0.30 0.26 0.31
Above concluding remarks can be improved by carrying out further investigation with different wrapping patterns, i.e. wrapping of GFRP fabrics in only effective bending zone without extending to the supports and providing the vertical/diagonal strips of GFRP fabrics in the shear zone for the optimal performance.
from both the design proposals. Therefore, both the predictions have to be improved in order to get the predicted values closer to the experimental ones. However, both predictions can be used safely to obtain the ultimate flexural strength of the strengthened beams as these values are lower than the experimental ones. But, the design based on these predictions may not be economical.
References [1] Saadatmanesh H, Ehsani MRRC. Beams strengthened with FRP plates I: experimental study. J Struct Eng 1991;117(11):3417–33. [2] Sharif A, Al-Sulaimani GJ, Basunbul IA, Baluch MH, Ghaleb BN. Strengthening of initially loaded RC beams using FRP plates. ACI Struct J 1994;91(2):160–8. [3] Nanni A, Norris MS. FRP Jacketed Concrete under flexure and combined flexuralcompression. Construct Build Mater 1995;9(5):273–81. [4] Li LJ, Guo YC, Liu F, Bungey JH. An experimental and numerical study of the effects of thickness and length of CFRP on performance of repaired reinforced concrete beams. Construct Build Mater 2006;20(10):901–9. [5] Grace NF, Abdel-Sayed G, Soliman AK, Saleh KR. Strengthening of reinforced concrete beams using fibre reinforced polymer (FRP) laminates. ACI Struct J 1999;96(5):865–74. [6] Kachlakev D, Mercurry DD. Behaviour of full-scale reinforced concrete beams retrofitted for shear and flexure with FRP laminates. Compos Part B Eng 2000;31:445–52. [7] Sheikh SA. Performance of concrete structures retrofitted with fibre reinforced polymers. Eng Struct 2002;24:869–79. [8] Al-Tamimi AK, Hawileh R, Abdalla J, Rasheed HA. Effects of ratio of CFRP plate length to shear span and end anchorage on flexural behaviour of SCC RC beams. J Compos Constr 2011;15(6):908–19. [9] Ahmed E, Sobuz HR, Sutan NM. Flexural performance of CFRP strengthened RC beams with different degrees of strengthening schemes. Int J Phys Sci 2011;6(9):2229–38. [10] Abdesselam Z. Numerical modeling of strengthened concrete beams. Int J Civ Struct Eng 2012;2(4):1122–8. [JOUR Integrated Publishing Association]. [11] Onal Mustafa M. Strengthening reinforced concrete beams with CFRP and GFRP.
6. Conclusions An attempt has been made to study the behaviour of RC beams retrofitted with different layers and laying patterns of externally wrapped GFRP fabrics and to get the trend of increase in their flexural strength. Though the present study is not so extensive, still an endeavour has been made to illustrate the following conclusions within the frame work of the present investigation. 1. The flexural strength of the retrofitted RC beams increases with the increase in number of layers in all the laying patterns. However, the failure pattern gradually changes from ductile to brittle behaviour with increase in the number of layers of GFRP sheet in any lay-up pattern. 2. Increase in the flexural strength of the retrofitted RC beams with reference to that of the beam without GFRP sheets is different for different laying patterns. RC beams in which the bottom portion and 151
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Adv Mater Sci Eng 2014:1–8. [12] George RK, Ashokkumar T, John A. Study of strength development in reinforced concrete beams retrofitted by different types of Fiber Reinforced Polymers. Int J Innov Sci Eng Technol 2015;2(10):671–6. [13] Norris T, Saadatmanesh H, Ehsani MR. Shear and flexural strengthening of R/C beams with carbon fibre sheets. J Struct Eng 1997;123(7):903–11. [14] Ramana VPV, Kant T, Morton SE, Dutta PK, Mukherjee A, Desai YM. Behaviour of CFRPC strengthened reinforced concrete beams with varying degrees of strengthening. Compos Part B 2000;31:461–70. [15] Bencardino F, Spadea G, Swamy RN. Strength and ductility of reinforced concrete beams externally reinforced with carbon fibre fabric. Struct J 2002;99(2):163–71. [16] Alagusundaramoorthy P, Harik IE, Choo CC. Flexural behaviour of R/C beams strengthened with carbon fibre reinforced polymer sheets or fabric. J Compos Constr 2003;7(4):292–301. [17] Hsu CT, Punurai W, Zhang Z. Flexural and shear strengthening of RC beams using carbon fiber reinforced polymer laminates. 2003;211:89–114. [Special Publication]. [18] Bencardino F, Colotti V, Spadea G, Swamy RN. Shear behaviour of reinforced concrete beams strengthened in flexure with bonded carbon fibre reinforced polymers laminates. Can J Civ Eng 2005;32(5):812–24. [NRC Research Press]. [19] Zhang A, Jin W, Li G. Behaviour of pre-loaded RC beams strengthened with CFRP laminates. J Zheijang Univ Sci A 2006;7(3):436–44. [20] Valivonis J, Skuturna T. Cracking and strength of reinforced concrete structures in flexure strengthened with carbon fibre laminates. J Civ Eng Manag 2007;XIII(4). [21] Bahn BY, Harichandran RS. Flexural behaviour of reinforced concrete beams strengthened with CFRP sheets and epoxy mortar. J Compos Constr 2008;12(4):387–95. [22] Sobuz HR, Ahmed E, Hassan NMS, Uddin MA. Use of carbon fibre laminates for strengthening reinforced concrete beams in bending. Int J Civ Struct Eng 2011;2(1):67–83. [23] Obaidat YT, Heyden S, Dahlblom O, Abu-Farsakh G, Abdel-Jawad Y. Retrofitting of reinforced concrete beams using composite laminates. Construct Build Mater 2011;25(2):591–7. [24] Li G, Guo Y, Sun X. Investigation on flexural performance of RC beams flexurally strengthened by side-bonded CFRP laminates. Open Civil Eng J 2012;6:26–32. [25] Alferjani MBS, Samad AAA, Elrawaff BS, Mohamad N, Hilton M, Saiah AAS. Use of carbon fibre reinforced polymer laminate for strengthening reinforced concrete beams in shear: a review. Int Refereed J Eng Sci 2013;2(2):45–53. [26] Raju A, Mathew LA. Retrofitting RC beams using FRP. Int J Eng Res Technol 2013;2(1):1–6. [27] Kharatmol R, Sananse P, Tambe R, Khare RJ. Strengthening of beams using carbon fibre reinforced polymer. Int J Emerg Eng Res Technol 2014;2(3):119–25. [28] Chiew SP, Sun Q, Yu Y. Flexural strength of RC beams with GFRP laminates. J Compos Constr 2007;11(5):497–506. [29] Amitha NR, Vrinda T. Retrofitting of reinforced concrete beams using carbon fibre composite laminate and glass fibre composite laminate. Indian J Appl Res 2013;3(7):188–301. [30] Dhanu MN, Revathy D, Lijina Rasheed SS. Experimental and numerical study of retrofitted RC beams using FRP. Int J Eng Res Gen Sci 2014;l2(3). [31] Mini KM, Alapatt RJ, David E, Radhakrishnan A, Cyriac MM, Ramakrishnan R. Experimental study on strengthening of RC beam using glass fibre reinforced composite. Struct Eng Mech 2014;50(3):275–86. [32] Aravind N, Samanta AK, Thanikal JV, Singha Roy DK. Experimental study on precracked reinforced concrete beams strengthened with externally bonded GFRP composites. Int J Multidiscip Res Dev 2015;2(2):219–24. [33] Jain N, Sikka VK. Strengthening of RC beams with externally bonded GFRPS. J Mech Civil Eng 2015;12(2):139–42. [34] Khot SR, Jadhav HS. Repair of damaged reinforced concrete beam externally bonded with GFRP plates. Int Res J Eng Technol 2015;2(3):1777–84. [35] Rushad ST, Duggal SK, Shukla KK. Experimental investigations of RC beams strengthened with 4-layered symmetric cross-ply (scp) GFRP laminates. Int J Res Eng Technol 2015;4(13):431–4. [36] Subramani T, Jayalakshmi J. Analytical investigation of bonded glass fibre reinforced polymer sheets with reinforced concrete beam using Ansys. Int J Appl Innov Eng Manag 2015;4(5):105–12. [37] Patel TH, Parikh KB. Strengthening of reinforced concrete beams with fibre reinforced polymer sheets with different configurations in shear and flexure. Int J Emerg Technol Adv Eng 2016;6(1):156–60. [38] Smith ST, Teng JG. FRP-strengthened RC beams I: review of debonding strength models. Eng Struct 2002;24(4):385–95. [39] Arduini M, Nanni A, Romagnolo M. Performance of decommissioned RC girders strengthened with FRP laminates. ACI Struct J 2002;99(5):652–9. [40] Kang THK, Howell J, Sanghee K, Lee DJ. A state of the art review on debonding
[41] [42]
[43]
[44] [45]
[46]
[47]
[48]
[49] [50]
[51] [52] [53] [54] [55]
[56]
[57]
[58]
[59]
[60]
[61] [62]
[63]
[64] [65] [66]
152
failures of FRP laminates externally adhered to concrete. Int J Concr Struct Mater 2012;6(2):123–34. Arduini M, Di Tommaso A, Nanni A. Brittle failure in FRP plate and sheet bonded beams. ACI Struct J 1997;94(4):363–70. Malek AM, Saadatmanesh H, Ehsani MR. Prediction of failure load of R/C strengthened with FRP plate due to stress concentration at the plate end. ACI Struct J 1998;95(1):142–52. Ross CA, Jerome DM, Tedesco JW, Hughes ML. Strengthening of reinforced concrete beams with externally bonded composite laminates. ACI Struct J 1999;96(2):65–71. Sebastian WM. Significance of mid-span de-bonding failure in FRP-plated concrete beams. J Struct Eng 2001;127(7):792–8. Oehlers DJ. Development of design rules for retrofitting by adhesive bonding or bolting either FRP or steel plates to RC beams or slabs in bridges and buildings. Compos Part A 2001;32:1345–55. Aiello MA, Ombres L. Cracking and deformability analysis of reinforced concrete beams strengthened with externally bonded carbon fibre reinforced polymer sheets. J Mater Civ Eng 2004;16(5):392–9. Pham H, Al-Mahaidi R. Experimental investigation into flexural retrofitting of reinforced concrete bridge beam using FRP composites. Compos Struct 2004;66(4):617–25. ACI:440-2R-08. Guide for the design and construction of externally bonded FRP systems for strengthening concrete structures. Farmington Hills, Mich., USA: American Concrete Institute; 2008. International Federation of Structural Concrete (fib). Externally bonded FRP reinforcement for RC structures. Technical report bulletin 14. 2001. Japan Society of Civil Engineers. Recommendations for upgrading of concrete structures with use of continuous fibre sheet. Concrete engineering series 41. JSCE; 2001. The Concrete Structure Society. U.K. national structural concrete specification for building construction. 2004. [Camberly, Surrey, UK]. ISIS Canada. An introduction to FRP strengthening of concrete structures. ISIS educational module 4. 2004. IS:456-2000. Code of practice for plain and reinforced concrete. New Delhi: Bureau of Indian Standards; 2000. IS: 455. Portland slag cement-specification (fourth revision). 1989. [Reaffirmed in 1995]. IS: 4031. Indian standard specification methods of physical tests for hydraulic cement: part 11, determination of density. New Delhi: Bureau of Indian Standards; 1988. [Reaffirmed in 2005]. IS: 4031. Indian standard specification methods of physical tests for hydraulic cement: part 2, determination of fineness by specific surface by Blaine Air Permeability method. New Delhi: Bureau of Indian Standards; 1999. [Reaffirmed in 2004]. IS: 4031. Indian standard specification methods of physical tests for hydraulic cement: part 4, determination of consistency of standard cement paste. New Delhi: Bureau of Indian Standards; 1988. [Reaffirmed in 2005]. IS: 4031. Indian standard specification methods of physical tests for hydraulic cement: part 5, determination of initial and final setting times. New Delhi: Bureau of Indian Standards; 1988. [Reaffirmed in 2005]. IS: 4031. Indian standard specification methods of physical tests for hydraulic cement: part 6, determination of compressive strength of hydraulic cement (other than Masonry cement). New Delhi: Bureau of Indian Standards; 1988. [Reaffirmed in 2005]. IS: 2386. Indian standard specification, methods of test for aggregates for concrete: part 1, particle size and shape. New Delhi: Bureau of Indian Standards; 1963. [Reaffirmed in 2002]. IS: 383. Indian standard specification for coarse and fine aggregate from natural sources. New Delhi: Bureau of Indian Standards; 1970. IS: 2386, Indian standard specification, methods of test for aggregates for concrete: part 3, specific gravity, density, voids, absorption and bulking. Bureau of Indian Standards, New Delhi, 1963 [Reaffirmed in 2002]. IS: 2386. Indian standard specification, methods of test for aggregates for concrete: part 4, mechanical properties. New Delhi: Bureau of Indian Standards; 1963. [Reaffirmed in 2002]. IS: 1786. High strength deformed bars and wires for concrete reinforcement — specification. New Delhi: Bureau of Indian Standards; 2008. IS:10262. Concrete mix proportioning- guidelines. New Delhi: Bureau of Indian Standards; 2009. ASTM D 7565-10. Standard test method for determining tensile properties of fibre reinforced polymer matrix composites used for strengthening of civil structures. 2017.
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Strengthening of RC Beams Using Externally Bonded Fibre Reinforced Polymer Composites
T
⁎
A.N. Nayaka, , A. Kumaria, R.B. Swainb a b
Department of Civil Engineering, Veer Surendra Sai University of Technology, Burla, 768018 Sambalpur, Odisha, India Sambalpur University, Burla, Sambalpur, Odisha, India
A R T I C LE I N FO
A B S T R A C T
Keywords: Design proposals Failure modes Flexural strengthening GFRP fabrics RC beams
An experimental study is presented on the behaviour of reinforced concrete (RC) beams retrofitted externally with glass fibre reinforced polymer (GFRP) fabrics. Out of ten beams, one beam without GFRP and nine beams wrapped in various lay-up patterns with one, two, three and four layers of GFRP fabrics have been tested for flexure under two-point loading. Loads corresponding to the first crack/delamination and ultimate failure of the beams have been recorded and types of failure have also been observed. Load versus deflection graphs have been plotted at salient locations of beams. Thereafter, a critical discussion has been made with respect to increase in the flexural strength of retrofitted beams as compared to the control beam in order to explore the optimal use of GFRP fabrics for strengthening the RC beams. In addition, a design proposal has been developed in extension to IS: 456-2000 to predict the ultimate design strength of RC beams strengthened with fibre reinforced polymer (FRP) fabric sheets. Thereafter, the values of the experimental flexural strength of the strengthened RC beam have been compared with the corresponding values of design flexural strength computed from present formulation and ACI: 440-2R-08 for its validation. The results obtained from the present experimental study show that flexural strength of the strengthened RC beams increases with increase in number of layers for all lay-up patterns. However, the beams wrapped with two layers GFRP fabrics in the tension face and half of the both sides below neutral axis show superior performance with respect to flexural strength, ductility and economy.
1. Introduction The major problem faced by civil engineers worldwide is a premature deterioration in concrete structures. FRP fabrics/laminates have been introduced as the advanced materials for strengthening/retrofitting of existing concrete structures since more than two decades due to their high strength, low weight, corrosion resistance, high fatigue resistance, easy and rapid installation and minimal change in structural geometry. A lot of research works have been done and some field applications have also been conducted on the strengthening of RC beams/ girders using externally bonded FRP laminates/sheets. Several investigators [1–12] carried out experimental investigations on RC beams/girders retrofitted with Carbon/Glass/Aramid fibre reinforced polymer (CFRP/GFRP/AFRP) composites in order to study their efficacy. Most of the experimental works were carried out on CFRP fabrics/ sheets/laminates in strengthening of RC structures which showed that the strengthening with externally wrapped CFRP laminates/sheets in the tension face significantly increased the strength in bending, reduced the deflections as well as crack width of the RC beams in comparison to
⁎
other types of FRPs [13–27]. There are also some notable studies related to the application of externally wrapped GFRP composites for strengthening the RC beams, which showed that U wrapping of GFRP sheet is an effective way to enhance the flexural capacity of RC beams [28–37]. However, most often the strengthened beams with FRP composite failed in a brittle way, mainly due to the loss of contact between the composite material and the concrete [38–40]. Further, various theoretical calculations and numerical simulations were also proposed by various researchers [14,41–47] in order to estimate the ultimate load carrying capacity, flexural strength and ductility of FRP strengthened RC beams and found to be in good agreement with the experimental results. In addition to the above research works, several design guidelines [48–52] in various countries have been brought forth in these days for strengthening/retrofitting of concrete structures using externally wrapped FRP sheets. All the above design guidelines are based on the traditional sectional analysis called “plane sections before bending remain plane after bending”. However, there is discrepancy in the design results due to differences in adopting safety factors. Moreover,
Corresponding author. E-mail address: [email protected] (A.N. Nayak).
https://doi.org/10.1016/j.istruc.2018.03.004 Received 8 December 2017; Received in revised form 4 March 2018; Accepted 6 March 2018 Available online 07 March 2018 2352-0124/ © 2018 Institution of Structural Engineers. Published by Elsevier Ltd. All rights reserved.
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topographical and ecological conditions as well as social background are different in each country and the prerequisites for design of RC structures using externally bonded FRP laminates may not be same. Therefore, a thorough experimental investigation is required in a country to upgrade its design guidelines time to time so that the discrepancy between the experimental results and the results obtained from the design guidelines will reduce. Therefore, the present investigation aims to study the behaviour of the flexural strengthening of RC beams using externally bonded GFRP fabrics. The study includes the effects of different parameters such as number of layers and wrapping scheme/patterns of GFRP fabric on strength, deflection and ductility of RC beams. In addition to the above experimental work, a theoretical model for flexural strengthening is also developed with the extension of IS: 456-2000 [53]. The ultimate flexural strength obtained from the experimental investigation is also compared with those predicted from the proposed design proposal and ACI: 440-2R-08 [40].
Percentage passing
100 80 60 40
Min IS:383 [61] (Zone-III) Max IS:383 [61] (Zone-III)
20
Fine Aggregate
0 0.15
0.3
0.6 1.18 Sieve size (mm)
2.36
4.75
Fig. 1. Grading analysis of fine aggregate.
2. Experimental investigation
120
In order to study the structural performance of RC beams strengthened with GFRP fabrics, ten beams were prepared, out of which one without GFRP fabric and the remaining nine beams wrapped with GFRP fabrics. All the RC beams were tested under two-point loading. Accordingly, characterization of materials such as cement, aggregates, steel and GFRP fabric, preparation of specimen, wrapping of GRFP fabrics on beams, testing and observations are presented and discussed in the following sub-sections.
Percentage passing
100
2.1. Testing of materials
80 60 Min-IS: 383 [61]for 20mm nominal size Max-IS: 383 [61] for 20mm nominal size Coarse Aggregate
40 20
2.1.1. Cement Fresh Ultratech Portland Slag Cement (PSC) conforming to IS: 4551989 [54] was used for the preparation of all beam specimens. The required physical and mechanical properties of cement were determined in accordance to Indian standard specifications [55–59]. The test results of physical and mechanical properties of cement along with the standard test methods are presented in Table 1. It is found that the above cement satisfies the specification of PSC as per IS: 455-1989 [54].
0 4.75
10 20 Sieve size(mm)
40
Fig. 2. Grading analysis of 20 mm coarse aggregate.
the requirements in accordance to IS: 383-1970 [61]. From Figs. 1 and 2, it is observed that the grading of fine aggregate and 20 mm coarse aggregate are satisfying the grading limits in accordance to IS: 3831970 [61]. Further, other physical and mechanical properties such as bulk density, specific gravity, water absorption, impact value, abrasion value and crushing value were obtained as per IS: 2386-1963 (part 3 and part 4) [62,63] and the results of the same are furnished in Table 2 along with test methods. From this table, it is seen that these properties are within the limit specified by IS-383-1970 [61].
2.1.2. Aggregates Sand collected from local river was used as fine aggregate. The Crushed granite of 20 mm nominal size was used as coarse aggregates for preparing concrete. The sieve analysis of fine aggregate and coarse aggregate were carried out as per IS: 2386-1963 (Part 1) [60] and the results of the same are shown in Figs. 1 and 2, respectively along with Table 1 Physical and mechanical properties of cement. Properties
Test method
Test results
IS:455 limit [54]
Fineness (cm2/g)
IS 4031: 1988 (part-2) [56] IS 4031: 1988 (part-11) [55] IS 4031: 1988 (part-4) [57] IS 4031: 1988 (part-5) [58]
3300 3.14
Not less than 2250 –
32
–
105 535
Not less than 30 Not more than 600
Specific gravity Standard consistency (%) Setting time (min) Initial setting time (min) Final setting time (min) Compressive strength (MPa) 3 days 7 days 28 days
2.1.3. Steel High yield strength deformed (HYSD) bars of Fe415 grade were used as the reinforcement for the preparation of RC beam specimens. The mechanical properties of the reinforcing steel bar were obtained through tensile strength test in the Universal Testing Machine (UTM) confirming to IS: 1786-2008 [64]. The stress-strain curve obtained from the tensile strength test of HYSD bar of 8 mm diameter is shown in Fig. 3. From the tensile strength test, the average yield strength, ultimate strength and percentage elongation of HYSD bars were obtained as 428.6 MPa, 506.6 MPa and 21.7, respectively. 2.1.4. GFRP fabrics A GFRP fabric used in the present study is a fabric of 0.275 mm thick and is made up of stitching cross glass fibres. Four coupons were prepared by binding four layers of GFRP fabrics with binding materials Epoxy and Hardener in the ratio of 9:1. The top view, side view and
IS 4031: 1988 (part-6) [59] 16.87 22.33 36.26
Not less than 16 Not less than 22 Not less than 33
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Table 2 Physical and mechanical properties of aggregates. Properties
Test method
Specific gravity Water absorption (%) Free surface moisture (%) Loose bulk density (kg/m3) Compact bulk density (kg/m3) Impact value (%) Abrasion value (%) Crushing value (%)
IS: IS: IS: IS: IS: IS: IS: IS:
2386 2386 2386 2386 2386 2386 2386 2386
(part-3) (part-3) (part-3) (part-3) (part-3) (part-4) (part-4) (part-4)
[62] [62] [62] [62] [62] [63] [63] [63]
Fine aggregate
Coarse aggregate
IS: 383 limit [61]
2.6 1.0 Nil 1443 1566 – – –
2.8 0.5 0.38 1448 1615 22.42 25.23 20.39
– – – – – 45 50 45
displacement at peak load, displacement at breaking load, stress at peak, strain at peak, stress at 0.2% yield, strain at 0.2% yield and Young's modulus. The above results are presented in Table 3. Average ultimate strength and ultimate elongation of the GFRP fabric are 236.5 MPa and 4.084%, respectively. It is worth mentioning that the elongation at the peak load is 4.069%, which is slightly less than the ultimate elongation. It indicates the brittle failure of GFRP.
500
Stress (Mpa)
400
300
2.2. Preparation of specimen
200
Concrete mix design was done for M25 grade concrete according to IS: 10262-2009 [66]. All the RC beam specimens of size 120 mm × 150 mm × 1000 mm were prepared with M25 grade concrete and Fe415 grade steel. Three concrete cubes of size 150 mm were prepared along with the preparation of each beam specimen. The beams and cubes were allowed for 28 days curing in water at 27 ± 2 °C temperature. The beam with dimensions and reinforcement details is presented in Fig. 5.
100
0 0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
Strain Fig. 3. Stress-strain curve of HYSD bar.
2.3. Wrapping of GFRP fabrics
photograph of the prepared coupons along with its dimension are presented in Fig. 4(a), (b) and (c) respectively. All the coupons were tested in the INSTRON machine as per ASTM D7565-10-2017 [65] in order to obtain its properties like peak load, breaking load,
150mm
50mm 25 mm
50mm
In order to fulfil the objective, ten RC beams were tested with twopoint loading. Out of which, nine RC beams were wrapped with GFRP fabrics in different layers and lay-up patterns and one RC beam was
(a) Top View Gauge length 4 layers of GFRP fabrics Aluminium Plate (b) Side View
(c) photograph of GFRP coupon Fig. 4. Details of GFRP coupon.
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Table 3 Test results of GFRP coupons. Sp.no.
Peak load (kN)
Breaking load (kN)
Displacement at peak (mm)
Displacement at break (mm)
Stress at peak (MPa)
Strain at peak (%)
Stress at 0.2% yield (MPa)
Strain at 0.2% yield (%)
Young's modulus (MPa)
1 2 3 4 Mean
7.784 6.157 7.644 7.535 7.280
7.784 6.804 7.644 7.535 7.442
6.251 5.942 6.080 6.138 6.103
6.251 6.034 6.080 6.138 6.126
254.2 203.8 248.8 239.2 236.5
4.168 3.961 4.054 4.092 4.069
104.90 86.22 112.90 101.70 101.40
1.270 1.095 1.318 1.239 1.231
9714 9675 9583 9928 9825
load/delamination load. Then the load was applied up to the failure of the beam. The deflections corresponding to the respective loads at three salient points i.e. L/3, L/2 & 2L/3 of the beams were recorded by fixing three dial gauges at these locations from the left support, where L is the centre to centre distance between both the supports. During the testing it was observed that all the ten beams showed almost similar behaviour in the initial stage of loading. In case of the beam BT00, the first hair crack occurred at the first load point (L/3) at a load of 38.0 kN. Thereafter, the longitudinal reinforcement started yielding with increase in load due to which the crack got widened. Finally, flexural failure occurred due to complete yielding of the longitudinal reinforcement and then crushing of concrete in compression zone at a load of 48.0 kN as expected. The above failure is shown in Fig. 10. In the beam BT11 (1 layer GFRP at bottom and 25 mm on both sides), the first crack appeared at a load of 46.3 kN with partial rupture of fibre at the middle third of the bottom portion due to the yielding of longitudinal reinforcement. With further increase in load, the beam finally failed due to complete yielding of longitudinal reinforcement and rupture of GFRP fabric at the bottom and thereby crushing of concrete at the top at a load of 50.7 kN indicating flexural failure (Fig. 11). The beam BT12 (2 layers of GFRP at the bottom and 25 mm on both sides) showed almost similar behaviour as in case of BT11. When the load gradually increased, the longitudinal reinforcement started yielding due to which the tearing of GFRP started at the bottom part and side vertical cracks initiated from the tearing of GFRP in the flexural zone at a load of 61.8 kN. Then, the yielding of longitudinal reinforcement went on with increase in load due to which the tearing of GFRP increased and side vertical cracks got widened. Finally, the
kept without GFRP fabric for reference. Before wrapping with GFRP fabrics in wet lay-up system, a standard procedure was followed to ensure a well prepared concrete surface for proper bonding between concrete and GFRP fabric. The binding material was brushed on the prepared concrete surface. Then, wrapping of GFRP was done layerwise and pressed with a roller to remove air void. The beam without GFRP fabric was designated as BT00. From the remaining nine beams wrapped with GFRP fabrics, four beams were wrapped fully with GFRP fabrics at the bottom portion and 25 mm height at both sides from the bottom in one, two, three and four layers and were designated as BT11, BT12, BT13 and BT14, respectively. Similarly, another four beams were wrapped fully with GFRP fabrics at the bottom portion and lower half (75 mm) of both sides in one, two, three and four layers and were designated as BT21, BT22, BT23 and BT24, respectively. For the remaining one beam, the bottom and two sides were wrapped completely with one layer of GFRP, which was designated as BT31. A typical wrapping of the beams with GFRP fabric is shown in Fig. 6(a) and (b). The detail wrapping scheme of GFRP fabrics with different layers are shown in Fig. 7. Finally, the specimens were kept for 7 days air curing at a temperature of 27 ± 2 °C before the testing.
2.4. Testing and observation The beam specimens were tested in the Universal Testing Machine (UTM-1000 kN) under two-point loading. The schematic diagram of experimental test set up is shown in Fig. 8 and the photograph of experimental test set up in UTM is shown in Fig. 9. The load at which the first visible crack/delamination appeared was recorded as the cracking
150 mm
120 mm
4-8 mmØ
(a) Cross Section 1000 mm
2- legged 8mm dia. vertical Stirrups @200mm c/c (b) Longitudinal Section Fig. 5. Dimensions and reinforcement details of RC beams.
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(a) GFRP Fabrics
(b) Beam surface. Fig. 6. Wrapping of beam with GFRP fabric.
flexural failure occurred due to complete yielding of longitudinal reinforcement and tearing of GFRP and then crushing of concrete in compression zone at a load of 68.8 kN (Fig. 12). In BT13 (3 layers of GFRP at the bottom and 25 mm on both sides), first crack developed at a load of 67.2 kN and then the tearing of GFRP at mid-span of the bottom portion started at a load of 70.0 kN. The failure of the beam was observed at a load of 96.0 kN with the development of wide vertical crack extending from the bottom to top at mid-span and complete debonding of GFRP fabrics from concrete in the middle third portion without crushing of concrete at the top indicating shear failure (Fig. 13). In BT14 (4 layers of GFRP at the bottom portion and 25 mm on both sides), diagonal shear crack initiated from the top portion of the beam near left load point at a load of 85.0 kN. With increase in load, the crack got widened and moved making an angle of about 45° with the beam axis towards the left support up to level of the retrofitting portion (25 mm from bottom) and moved horizontally towards left end of beam. Finally, the failure occurred at a load of 109.5 kN due to the debonding of GFRP fabrics from concrete surface indicating shear failure (Fig. 14). In BT21 (1 layer of GFRP at the bottom and 75 mm on both sides), the first crack developed at 63.5 kN at mid-span. With increase in load, the longitudinal reinforcement started yielding due to which the tearing of GFRP sheet was observed in the tension face in the flexural zone and the crack got widened. Finally, the flexural failure of the beam occurred
due to complete yielding of longitudinal reinforcement and tearing of GFRP fabrics in the tension face and subsequent crushing of concrete in the compression face at a load of 77.4 kN (Fig. 15). The beam BT22 showed the similar behaviour as the beams BT11, BT12 and BT21. With gradual increase in load, the longitudinal reinforcement started yielding which initiated the tearing of GFRP sheet and vertical crack in the flexural zone at a load of 80.0 kN. Finally the failure occurred due to complete yielding of the longitudinal reinforcement and tearing of GFRP sheet in the tension face and subsequent crushing of concrete in the compression face in the flexural zone at a load of 95.4 kN indicating flexural failure (Fig. 16). In BT23 (3 layers of GFRP at the bottom and 75 mm on both sides) the debonding of GFRP fabrics started at 60.0 kN and two inclined cracks initiated from the top of the beam at L/3 and 2L/3 load points at load of 70.0 kN. With an increase in load, both the cracks got widened and moved downward diagonally towards both the supports. Finally, the beam failed due to the combined effects of the widening of both cracks and tearing of GFRP fabrics in the bottom portion and crushing of concrete in compression face of mid-span at a load of 115.2 kN indicating flexure-shear failure (Fig. 17). In BT24 (4 layers of GFRP at the bottom and 75 mm on both sides) the first crack appeared at the loading point of L/3 at a load of 81.8 kN and propagated downward diagonally towards the left support with further increase in load. Thereafter, the debonding of GFRP fabrics started at 105.0 kN. Finally, complete separation of GFRP sheets from the beam 141
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8 mmØ @90mm c/c
25 mm 1 layer GFRP
8 mmØ @90mm c/c
8 mmØ @90mm c/c
1 layer GFRP
3 layer GFRP
(g) BT22
(h) BT23 120 mm
8 mmØ @90mm c/c
150 mm
150 mm
8 mmØ @90mm c/c 75 mm
2 layer GFRP
120 mm
4-8 mmØ
4-8 mmØ
75 mm
(f) BT21
(e) BT14
120 mm
4-8 mmØ
75 mm
4 layers GFRP
(d) BT13
120 mm
4-8 mmØ
25 mm
25 mm
150 mm
8 mmØ @90mm c/c
8 mmØ @90mm c/c
3 layers GFRP
(c) BT12
150 mm
4-8 mmØ
4-8 mmØ
8 mmØ @90mm c/c
2 layers GFRP
120 mm 150 mm
150 mm
120 mm
4-8 mmØ
25 mm
(b) BT11
(a) BT00
150 mm
4-8 mmØ
150 mm
8 mmØ @90mm c/c
150 mm
150 mm
4-8 mmØ
120 mm
120 mm
120 mm
120 mm
4-8 mmØ
8 mmØ @90mm c/c
75 mm 4 layer GFRP
1 layer GFRP
(j) BT31
(i) BT24
Fig. 7. Details of wrapping of beams with different layers and lay up patterns of GFRP.
load, the horizontal tearing of GFRP sheets at the bottom two edges and separation of bottom concrete cover with GFRP sheets from the beam near right support due to shear was observed leaving the beam as a simple RC beam at a load of 101.2 kN. Finally, the beam failed at the same load like simple RC beam due to yielding of the longitudinal reinforcement and subsequent crushing of concrete in the compression face near the load point. The failure of the beam BT31 is shown in
was observed in the left third portion. Then the beam failed in shear at a load of 140.0 kN due to development of a wide diagonal cracks and rupture of GFRP fabrics with bursting sound indicating shear failure (Fig. 18). In BT31 (bottom and both sides up to full depth wrapped with 1 layer of GFRP), the debonding of GFRP sheet started with a load of 90.0 kN near the right support of the beam. With further increase in
Load
Load
L/3
L/3
L/3
Dial gauge Fig. 8. Schematic diagram of experimental test set up.
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beyond which there is a decrease in load to 40.6 kN with increase in deflections up to 23 mm showing sufficient plasticity. In the beam BT12, the deflection increases up to 7 mm with an increase in load up to 68.0 kN. Further there is a sudden decrease in load by 11.0 kN with very little increase in deflection. Thereafter, the deflection of the beam increases up to 22 mm without further increase in load showing sufficient plasticity. On the other hand, for the beam BT13, load increases up to peak load of 96.0 kN with increase in deflection up to 14 mm and then decreases to 63.0 kN with very little increase in deflection without showing any plasticity. In case of BT14, with increase in the number of layers up to 4 layers, the load increases up to 109.0 kN (peak load) with the increase in deflection up to 15 mm. Thereafter, there is a sudden decrease in load to 73.0 kN without further increase in deflection showing brittleness. Both the beams BT13 and BT14 show the similar trend and have a brittle failure. In the beam BT21, deflection increases up to 10 mm with increase in load up to 77.0 kN, then increases up to 15 mm with gradual decrease in load up to 65.0 kN and finally increases up to 23 mm without any change in load showing sufficient ductility. With the addition of two similar layers of GFRP fabrics, the beam BT22 shows the similar trend as in the case of BT21 with the higher ultimate load, i.e. 95.0 kN. The load increases up to 95.0 kN (peak load) with the increase in deflection up to 9 mm and then gradually decreases to 60.0 kN with an increase in deflection up to 23 mm, i.e. significant increase in deflection with gradual decrease in load. Hence, the beam fails showing sufficient ductility. However, in the case of the beam BT23 the load increases up to 115.0 kN with an increase in deflection up to 13 mm and then suddenly decreases up to nearly 72.0 kN with very little increase in deflection showing brittle behaviour. Thereafter, there is very little increase in load with an increase in deflection up to 27 mm and finally, the beam fails at a load of 69.0 kN. The similar trend is observed in the case of the beam BT24, i.e. retrofitted with 4 numbers of similar layers. The load increases up to 140.0 kN with an increase in deflection up to 17 mm and then suddenly decreases to nearly 75.0 kN without any appreciable increase in deflection showing brittle behaviour. Then, deflection increases up to 28 mm with a marginal decrease in load and the beam breaks at a load of 71.0 kN. It is clearly verified during testing that the energy is released suddenly with a bursting sound in BT24. The separation of GFRP fabrics with complete debonding from the concrete surface is also observed in this case. From Figs. 20–22, it is inferred that BT24 shows more brittleness than BT23. On the other hand, in the beam retrofitted with 1 layer of GFRP fabric in all three sides (BT31), the deflections at L/3 and L/2 locations (Figs. 20–22) increases to a maximum value of 8 mm with an increase in load up to the failure point
Fig. 9. Photograph of experimental test set up in UTM.
Fig. 19. The summary of the test results of all the beams are presented in Table 4. 3. Results and discussion In order to derive a meaningful conclusion of the experimental investigation of the RC beams retrofitted with the different layers and laying patterns of GFRP fabrics, the data recorded during the testing are interpreted in different ways. At first the load versus deflection curves for all the beams at specific locations i.e. at L/3, L/2 and 2L/3 are plotted and furnished in Figs. 20–22, respectively. From Figs. 20–22, it is observed that the load versus deflection curves at the three locations have shown the similar trend. The deflections of beam BT00 at L/3, L/2 and 2L/3 locations increases up to 7 mm only with increase in load up to the failure without showing any plasticity. With addition of 1 layer of GFRP fabric retrofitted in the bottom portion and 25 mm of both sides as in case of the beam BT11, the load increases up to 50.7 kN with increase in deflection up to 12 mm
Fig. 10. Failure of beam BT00.
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Fig. 11. Failure of beam BT11.
Fig. 12. Failure of beam BT12.
fabrics before its use. Since the wrapping of the beam with GFRP in all three sides develops the brittleness in comparison to other two laying patterns keeping the number of layers constant, it is not desirable where only flexural strengthening is required. But, when the beam is required for both flexural and shear strengthening, then it may be useful for wrapping all three sides of the beam to get better strength.
(101.0 kN) showing slightly brittle behaviour due to debonding of GFRP layer. The deflection at 2L/3 increases up to 15 mm with the increase in the load having a lower slope in comparison to other two locations (Fig. 21). From the above discussion, it is clear that when the number of layers of GFRP fabrics increases in any laying pattern, the brittleness gradually increases. Similarly, wrapping the GFRP fabrics in all three sides of the beam develops the brittleness in comparison to other two laying patterns keeping the number of layers constant. In order to obtain the increase in flexural strength of the retrofitted RC beams with reference to the RC beam (BT00), the ultimate flexural strength and its percentage increase in comparison to the RC beam without GFRP fabrics are calculated from the test data and furnished in Table 5. The percentage increase is the highest for BT24 followed by BT23, BT14, BT31, BT13, BT22, BT21, BT12 and BT11. It is worth mentioning that BT22 gives nearly two times the flexural strength of RC beams with sufficient ductility with only 2 layers of GFRP wrapped in the bottom and half of both sides. Therefore, it is very much essential to ascertain the increase in ultimate strength and failure mode of any beam retrofitted with GFRP
4. Theoretical investigation In order to develop an analytical model for predicting the flexural strength of RC beams strengthened with FRP, the traditional sectional analysis is carried out in extension of IS: 456-2000 [53]. The following assumptions are made to develop the above model in addition to the assumptions considered in IS 456-2000 [53]. 1. The strain compatibility is to maintain at the interface of FRP fabrics and concrete, i.e. no slip between FRP fabrics and concrete. 2. The elastic modulus of the FRP used in the analysis shall be considered from the tensile coupon test of FRP fabrics. 144
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Fig. 13. Failure of beam BT13.
Fig. 14. Failure of beam BT14.
The above three cases are presented in the following sub-sections in order to derive the expression of design flexural strength.
An under-reinforced section of FRP strengthened RC beam is considered for the analytical investigation. The expression of design flexural strength of RC beams strengthened on the tension face of beam by wrapping FRP is normally available in various design proposals. However, in practice, in addition to the tension face, both sides of beam are wrapped partially or fully in order to strengthen the beam. Therefore, in the present study, an analysis has been made to obtain the flexural strength of the retrofitted beams for three cases as follows:
4.1. Case-I: wrapping of FRP at the tension face of the RC beam The cross-section of RC beam strengthened with FRP at the tension face of the beam, strain diagram and stress diagram for Case-I are shown in Fig. 23. From Fig. 23, the following relations can be obtained.
• Wrapping of FRP at the bottom face of the beam, i.e. in the tension face (Case-I) • Wrapping of FRP on both sides up to the section below the neutral •
axis and at the bottom face of the beam, i.e. in the tension zone (Case-II) Wrapping of FRP at the bottom part and two sides up to the depth above neutral axis i.e. in both the tension and compression zone (Case-III).
0.0035 ε2 = xu (d − x u )
(1)
0.0035 ε3 = xu (d + d′ − x u )
(2)
0.0035 ε4 = xu (d + d′ + t f − x u )
(3)
Now, the fibre strain is the average of ε3 and ε4 and can be written 145
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Fig. 15. Failure of beam BT21.
where b, d, d′, tf, xu, ε1, ε2, ε3 and ε4 are defined in Fig. 23, σf is the stress in fibre, Ef is the elastic modulus of fibre, fy is the yield stress in steel, fck is the characteristic stress of concrete, Ast is the cross-sectional area of main longitudinal reinforcement and Pt is the percentage of longitudinal steel reinforcement.
as:
εf =
ε3 + ε4 2
(4)
Therefore, stress in the fibre, σf, is expressed as
σf = εf Ef
(5)
Now, the depth of the neutral axis is obtained by equating compression and total tension and the same may be written as
0.87f y pt σf t f xu = + d 0.36fck 0.36fck d
4.2. Case-II: wrapping of FRP at the tension face and both side faces below the neutral axis The cross-section of the concrete beam strengthened with FRP at the tension face and both side faces below the neutral axis, strain diagram and stress diagram for Case II are indicated in Fig. 24. From Fig. 24, the following relations are obtained.
(6)
Now, the ultimate moment of resistance for FRP strengthened concrete beams is expressed as:
Mu =
0.87f y pt bd 2 100
t tf x d′ x ⎛1 − 0.42 u ⎞ + f bd 2σf ⎛1 + + − 0.42 u ⎞ d d d 2 d d⎠ ⎝ ⎠ ⎝
ε2 =
0.0035(h − x u − hf )
(7)
Fig. 16. Failure of beam BT22.
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xu
(8)
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Fig. 17. Failure showing tearing of GFRP of beam BT23.
Fig. 18. Failure of beam BT24.
ε3 =
0.0035(d − x u ) xu
(9)
ε4 =
0.0035(h − x u ) xu
(10)
ε5 =
Ff =
εfs = (11)
Ffs =
0.0035(2h + t f − 2x u ) 2x u
(12)
0.0035Ef (2h + t f − 2x u ) 2x u
(15)
2x u
0.0035Ef hf t f (2h + t f − 2x u − hf ) 2x u
(16)
Now, the depth of the neutral axis xu is evaluated by equating total compressive force and total tensile force and the same can be written as
Now, the stress in fibre, σf, is given by
σf =
0.0035(2h + t f − 2x u − hf )
Hence, the force on side wrapped FRP is given by
The fibre strain εf is the average of ε4 and ε5 and is expressed as
εf =
(14)
2x u
Similarly, the average strain of fibre along the side of the beam εfs is calculated by taking the average of ε2 and ε5 and given by
0.0035(h + t f − x u ) xu
0.0035Ef btf (2h + t f − 2x u )
0.87f y Ast + Ff + Ffs = 0.36fck bx u (13)
(17)
Now, the ultimate moment of resistance for FRP strengthened concrete beams may be expressed as:
Hence, the force on bottom FRP is given by 147
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Fig. 19. Failure of beam BT31.
Table 4 Summary of the test results. Beam type
28 days cube strength (MPa)
Cracking/delaminated load (kN)
Failure load (kN)
Contribution of strength from GFRP (kN)
Failure mode
BT00 BT11 BT12 BT13 BT14 BT21 BT22 BT23 BT24 BT31
30.5 30.7 30.7 30.4 33.7 33.8 31.7 32.9 32.2 30.8
38.0 46.3 61.8 67.2 85.0 63.5 80.0 70.0 81.8 90.0
48.0 50.7 68.8 96.0 109.5 77.4 95.4 115.2 140.0 101.2
– 2.7 20.8 48.0 61.5 29.4 47.4 67.2 92.0 53.2
Flexure failure Flexure failure Flexure failure Shear failure Shear failure Flexure failure Flexure failure Flexure-shear failure Shear failure Shear-flexure failure
140
100 80 60
100
40
80 60 40
20 0
BT00 BT11 BT12 BT13 BT14 BT21 BT22 BT23 BT24 BT31
120
Load (kN)
120
Load (kN)
140
BT00 BT11 BT12 BT13 BT14 BT21 BT22 BT23 BT24 BT31
20 0
5
10
15
20
25
30
35
Deflection (mm)
0 0
Fig. 20. Load vs. deflection at L/3 of all beams.
5
10
15
20
25
Deflection (mm) Fig. 21. Load vs. deflection at L/2 of all beams.
148
30
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160 BT00 BT11 BT12 BT13 BT14 BT21 BT22 BT23 BT24 BT31
140 120
Load (kN)
100 80 60
.
0.0035(2h + t f − 2xu )
The fibre strain is the average of ε4 and ε5 and
0.0035(2h + t f − 2x u )
εf =
(24)
2x u
Now, the stress in fibre, σf, is given by
0.0035Ef (2h + t f − 2x u )
σf =
(25)
2x u
Hence, the force on bottom FRP is given by
0 0
5
10
15
20
25
30
0.0035Ef btf (2h + t f − 2x u ) 2x u
Ffs =
0.0035Ef t f (h + t f − x u )2 (28)
xu
The effect of fibre in compression is neglected. Then the depth of the neutral axis ‘xu’ is obtained by equating total compressive force and total tensile force and the same may be written as
where h, hf, tf, xu, d, ε2, ε3, ε4 and ε5 are defined in Fig. 24, k is centroidal distance of force acting on a beam due to side fibres. Where
0.87f y Ast + Ff + Ffs = 0.36fck bx u
hf
(29)
Now, the ultimate moment of resistance for FRP strengthened concrete beams may be expressed as:
(19)
Mu = 0.87f y Ast (d − 0.42x u ) +
4.3. Case-III: wrapping of FRP at the tension face and both side faces above the neutral axis
0.0035Ef btf (2h + t f − 2x u ) 2x u
t ⎛h + f 2 ⎝
− 0.42x u⎞ ⎠ 0.0035Ef t f (h + t f − x u )2 + (h − k − 0.42x u ) xu
The cross-section of concrete beam strengthened with FRP at the tension face and both side faces above the neutral axis, strain diagram and stress diagram for Case III are indicated in Fig. 25. From Fig. 25, the following relations are obtained:
(30) where h, hf, tf, xu, d, ε2, ε3, ε4 and ε5 are defined in Fig. 25, k is the centroidal distance of force acting on a beam due to side fibre and is given by:
0.0035(x u − h + hf ) (20)
0.0035(d − x u ) xu
(27)
xu
Hence, the force on side wrapped FRP is given by
(18)
xu
0.0035(h + t f − x u )
εfs =
t ⎛h + f 2 ⎝
− 0.42x u⎞ ⎠ 0.0035Ef hf t f (2h + t f − 2x u − hf ) + (h + k − 0.42x u ) 2x u
2ε2 + ε5 × ε2 + ε5 3
(26)
2x u
Similarly, the average strain of fibre along the side of the beam is calculated by taking the average of ε2 and ε5 and given by
Fig. 22. Load vs. deflection at 2L/3 of all beams.
Mu = 0.87f y Ast (d − 0.42x u ) +
0.0035Ef btf (2h + t f − 2x u )
Ff =
35
Deflection (mm)
ε3 =
(23)
2x u
εf = 2xu can be written as
20
ε2 =
(22)
0.0035(2h + t f − 2x u )
ε5 =
40
k=
0.0035(h − x u ) xu
ε4 =
k=
(21)
h − xu 3
(31)
Table 5 Increase in flexural strength due to wrapping of GFRP fabrics. Beam type
Experimental ultimate moment of resistance (Mu) (kN-m)
% increase of Mu with reference to BT00
Remarks
BT00 BT11 BT12 BT13 BT14 BT21 BT22 BT23 BT24 BT31
8.00 8.45 11.46 16.00 18.25 12.83 15.90 19.20 23.33 16.87
0.0 5.6 43.2 100.0 128.1 61.0 98.7 140.0 191.6 110.8
Ductile failure Ductile failure Ductile failure Brittle failure Brittle failure Ductile failure Ductile failure Brittle failure Brittle failure Brittle failure
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Fig. 23. Stress-strain diagrams of FRP strengthened RC beam (Case-I).
5. Comparison between predicted and experimental results
where, As is the area of steel reinforcement, fs is the stress in the steel reinforcement, d is the distance between extreme compression fibre and centroid of tension reinforcement, β1 is the ratio between depth of equivalent rectangular stress block and depth of the neutral axis and ‘c’ is the distance between extreme compression fibre and neutral axis. Mnf is the contribution of the FRP reinforcement to the nominal flexural strength and is expressed as:
In order to validate the analytical model developed in the present study, values of the flexural strength predicted from the present design model for all the RC beams considered in the present study are compared with those obtained from experimental investigation and predicted from ACI:440-2R-08 [48]. Accordingly, the theoretical values of flexural strength of the ten RC beam considered in the experimental investigation are obtained from the present design model using Eqs. (7), (18) and (30). Similarly, the flexural strength of all above beams has been predicted from ACI: 440-2R-08 48 using the following equations.
ϕMn = ϕ ⌊Mns + φf Mnf ⌋
βc Mnf = Af f fe ⎛df − 1 ⎞ 2 ⎠ ⎝ ⎜
⎜
(34)
where, Af is the area of FRP, ffe is the effective stress in the FRP and df is the effective depth of FRP flexural reinforcement. Finally, the values of the flexural strength obtained from the experimental investigation and predicted from the present design proposal and ACI: 440-2R-08 48 for all the RC beams considered are presented in Table 6. From Table 6 it is found that, the ultimate flexural strength values of the strengthened RC beams predicted from present design proposal are in good agreement with those predicted from ACI:440-2R-08 48. But, the experimental values of the ultimate flexural strength of the strengthened beams are higher than those predicted
(32)
where, Mn is the nominal flexural strength, ϕ is the strength reduction factor for structural concrete equal to 0.90, φf is the strength reduction factor of FRP equal to 0.85 for flexure, Mns is the contribution of RC beam to the nominal flexural strength, which is expressed as:
βc Mns = As fs ⎛d − 1 ⎞ 2 ⎠ ⎝
⎟
⎟
(33)
Fig. 24. Stress-strain diagrams of FRP strengthened RC beam (Case-II).
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Fig. 25. Stress-strain diagrams of FRP strengthened RC beam (Case-III).
half of both sides (approximately tension zone) are wrapped with GFRP completely, shows better performance with respect to strength and ductility as compared to other two patterns, i.e. bottom portion and 25 mm of both sides, and bottom and full depth of both sides wrapped with GFRP. 3. The beams wrapped with 2 layers GFRP sheets in the tension zone of the beam (bottom portion and half of both sides) shows superior performance with respect to increase in flexural strength, failure pattern and economy in comparison to other retrofitted beams. 4. The ultimate flexural strength values of the strengthened RC beams predicted from the present model are in good agreement with those predicted from ACI: 440-2R-08 48 and lower than those obtained from experimental investigation, which needs further refinement of the present model.
Table 6 Comparison between theoretical and experimental results of flexural strength of strengthened RC beam. Beam type
BT BT BT BT BT BT BT BT BT BT
00 11 12 13 14 21 22 23 24 31
Experimental ultimate moment of resistance (Muex) (kN m)
8.00 8.45 11.46 16.00 18.25 12.83 15.90 19.20 23.33 16.87
Theoretical ultimate moment of resistance (Mu) ACI.2R.08 (Mu1)
Present method (Mu2)
4.68 5.20 5.58 5.97 6.31 – – – – –
4.562 5.04 5.404 5.704 5.98 5.01 5.593 5.936 6.208 5.244
Mu1 Muex
Mu2 Muex
0.58 0.62 0.49 0.37 0.34 – – – – –
0.57 0.59 0.47 0.35 0.32 0.39 0.35 0.30 0.26 0.31
Above concluding remarks can be improved by carrying out further investigation with different wrapping patterns, i.e. wrapping of GFRP fabrics in only effective bending zone without extending to the supports and providing the vertical/diagonal strips of GFRP fabrics in the shear zone for the optimal performance.
from both the design proposals. Therefore, both the predictions have to be improved in order to get the predicted values closer to the experimental ones. However, both predictions can be used safely to obtain the ultimate flexural strength of the strengthened beams as these values are lower than the experimental ones. But, the design based on these predictions may not be economical.
References [1] Saadatmanesh H, Ehsani MRRC. Beams strengthened with FRP plates I: experimental study. J Struct Eng 1991;117(11):3417–33. [2] Sharif A, Al-Sulaimani GJ, Basunbul IA, Baluch MH, Ghaleb BN. Strengthening of initially loaded RC beams using FRP plates. ACI Struct J 1994;91(2):160–8. [3] Nanni A, Norris MS. FRP Jacketed Concrete under flexure and combined flexuralcompression. Construct Build Mater 1995;9(5):273–81. [4] Li LJ, Guo YC, Liu F, Bungey JH. An experimental and numerical study of the effects of thickness and length of CFRP on performance of repaired reinforced concrete beams. Construct Build Mater 2006;20(10):901–9. [5] Grace NF, Abdel-Sayed G, Soliman AK, Saleh KR. Strengthening of reinforced concrete beams using fibre reinforced polymer (FRP) laminates. ACI Struct J 1999;96(5):865–74. [6] Kachlakev D, Mercurry DD. Behaviour of full-scale reinforced concrete beams retrofitted for shear and flexure with FRP laminates. Compos Part B Eng 2000;31:445–52. [7] Sheikh SA. Performance of concrete structures retrofitted with fibre reinforced polymers. Eng Struct 2002;24:869–79. [8] Al-Tamimi AK, Hawileh R, Abdalla J, Rasheed HA. Effects of ratio of CFRP plate length to shear span and end anchorage on flexural behaviour of SCC RC beams. J Compos Constr 2011;15(6):908–19. [9] Ahmed E, Sobuz HR, Sutan NM. Flexural performance of CFRP strengthened RC beams with different degrees of strengthening schemes. Int J Phys Sci 2011;6(9):2229–38. [10] Abdesselam Z. Numerical modeling of strengthened concrete beams. Int J Civ Struct Eng 2012;2(4):1122–8. [JOUR Integrated Publishing Association]. [11] Onal Mustafa M. Strengthening reinforced concrete beams with CFRP and GFRP.
6. Conclusions An attempt has been made to study the behaviour of RC beams retrofitted with different layers and laying patterns of externally wrapped GFRP fabrics and to get the trend of increase in their flexural strength. Though the present study is not so extensive, still an endeavour has been made to illustrate the following conclusions within the frame work of the present investigation. 1. The flexural strength of the retrofitted RC beams increases with the increase in number of layers in all the laying patterns. However, the failure pattern gradually changes from ductile to brittle behaviour with increase in the number of layers of GFRP sheet in any lay-up pattern. 2. Increase in the flexural strength of the retrofitted RC beams with reference to that of the beam without GFRP sheets is different for different laying patterns. RC beams in which the bottom portion and 151
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Adv Mater Sci Eng 2014:1–8. [12] George RK, Ashokkumar T, John A. Study of strength development in reinforced concrete beams retrofitted by different types of Fiber Reinforced Polymers. Int J Innov Sci Eng Technol 2015;2(10):671–6. [13] Norris T, Saadatmanesh H, Ehsani MR. Shear and flexural strengthening of R/C beams with carbon fibre sheets. J Struct Eng 1997;123(7):903–11. [14] Ramana VPV, Kant T, Morton SE, Dutta PK, Mukherjee A, Desai YM. Behaviour of CFRPC strengthened reinforced concrete beams with varying degrees of strengthening. Compos Part B 2000;31:461–70. [15] Bencardino F, Spadea G, Swamy RN. Strength and ductility of reinforced concrete beams externally reinforced with carbon fibre fabric. Struct J 2002;99(2):163–71. [16] Alagusundaramoorthy P, Harik IE, Choo CC. Flexural behaviour of R/C beams strengthened with carbon fibre reinforced polymer sheets or fabric. J Compos Constr 2003;7(4):292–301. [17] Hsu CT, Punurai W, Zhang Z. Flexural and shear strengthening of RC beams using carbon fiber reinforced polymer laminates. 2003;211:89–114. [Special Publication]. [18] Bencardino F, Colotti V, Spadea G, Swamy RN. Shear behaviour of reinforced concrete beams strengthened in flexure with bonded carbon fibre reinforced polymers laminates. Can J Civ Eng 2005;32(5):812–24. [NRC Research Press]. [19] Zhang A, Jin W, Li G. Behaviour of pre-loaded RC beams strengthened with CFRP laminates. J Zheijang Univ Sci A 2006;7(3):436–44. [20] Valivonis J, Skuturna T. Cracking and strength of reinforced concrete structures in flexure strengthened with carbon fibre laminates. J Civ Eng Manag 2007;XIII(4). [21] Bahn BY, Harichandran RS. Flexural behaviour of reinforced concrete beams strengthened with CFRP sheets and epoxy mortar. J Compos Constr 2008;12(4):387–95. [22] Sobuz HR, Ahmed E, Hassan NMS, Uddin MA. Use of carbon fibre laminates for strengthening reinforced concrete beams in bending. Int J Civ Struct Eng 2011;2(1):67–83. [23] Obaidat YT, Heyden S, Dahlblom O, Abu-Farsakh G, Abdel-Jawad Y. Retrofitting of reinforced concrete beams using composite laminates. Construct Build Mater 2011;25(2):591–7. [24] Li G, Guo Y, Sun X. Investigation on flexural performance of RC beams flexurally strengthened by side-bonded CFRP laminates. Open Civil Eng J 2012;6:26–32. [25] Alferjani MBS, Samad AAA, Elrawaff BS, Mohamad N, Hilton M, Saiah AAS. Use of carbon fibre reinforced polymer laminate for strengthening reinforced concrete beams in shear: a review. Int Refereed J Eng Sci 2013;2(2):45–53. [26] Raju A, Mathew LA. Retrofitting RC beams using FRP. Int J Eng Res Technol 2013;2(1):1–6. [27] Kharatmol R, Sananse P, Tambe R, Khare RJ. Strengthening of beams using carbon fibre reinforced polymer. Int J Emerg Eng Res Technol 2014;2(3):119–25. [28] Chiew SP, Sun Q, Yu Y. Flexural strength of RC beams with GFRP laminates. J Compos Constr 2007;11(5):497–506. [29] Amitha NR, Vrinda T. Retrofitting of reinforced concrete beams using carbon fibre composite laminate and glass fibre composite laminate. Indian J Appl Res 2013;3(7):188–301. [30] Dhanu MN, Revathy D, Lijina Rasheed SS. Experimental and numerical study of retrofitted RC beams using FRP. Int J Eng Res Gen Sci 2014;l2(3). [31] Mini KM, Alapatt RJ, David E, Radhakrishnan A, Cyriac MM, Ramakrishnan R. Experimental study on strengthening of RC beam using glass fibre reinforced composite. Struct Eng Mech 2014;50(3):275–86. [32] Aravind N, Samanta AK, Thanikal JV, Singha Roy DK. Experimental study on precracked reinforced concrete beams strengthened with externally bonded GFRP composites. Int J Multidiscip Res Dev 2015;2(2):219–24. [33] Jain N, Sikka VK. Strengthening of RC beams with externally bonded GFRPS. J Mech Civil Eng 2015;12(2):139–42. [34] Khot SR, Jadhav HS. Repair of damaged reinforced concrete beam externally bonded with GFRP plates. Int Res J Eng Technol 2015;2(3):1777–84. [35] Rushad ST, Duggal SK, Shukla KK. Experimental investigations of RC beams strengthened with 4-layered symmetric cross-ply (scp) GFRP laminates. Int J Res Eng Technol 2015;4(13):431–4. [36] Subramani T, Jayalakshmi J. Analytical investigation of bonded glass fibre reinforced polymer sheets with reinforced concrete beam using Ansys. Int J Appl Innov Eng Manag 2015;4(5):105–12. [37] Patel TH, Parikh KB. Strengthening of reinforced concrete beams with fibre reinforced polymer sheets with different configurations in shear and flexure. Int J Emerg Technol Adv Eng 2016;6(1):156–60. [38] Smith ST, Teng JG. FRP-strengthened RC beams I: review of debonding strength models. Eng Struct 2002;24(4):385–95. [39] Arduini M, Nanni A, Romagnolo M. Performance of decommissioned RC girders strengthened with FRP laminates. ACI Struct J 2002;99(5):652–9. [40] Kang THK, Howell J, Sanghee K, Lee DJ. A state of the art review on debonding
[41] [42]
[43]
[44] [45]
[46]
[47]
[48]
[49] [50]
[51] [52] [53] [54] [55]
[56]
[57]
[58]
[59]
[60]
[61] [62]
[63]
[64] [65] [66]
152
failures of FRP laminates externally adhered to concrete. Int J Concr Struct Mater 2012;6(2):123–34. Arduini M, Di Tommaso A, Nanni A. Brittle failure in FRP plate and sheet bonded beams. ACI Struct J 1997;94(4):363–70. Malek AM, Saadatmanesh H, Ehsani MR. Prediction of failure load of R/C strengthened with FRP plate due to stress concentration at the plate end. ACI Struct J 1998;95(1):142–52. Ross CA, Jerome DM, Tedesco JW, Hughes ML. Strengthening of reinforced concrete beams with externally bonded composite laminates. ACI Struct J 1999;96(2):65–71. Sebastian WM. Significance of mid-span de-bonding failure in FRP-plated concrete beams. J Struct Eng 2001;127(7):792–8. Oehlers DJ. Development of design rules for retrofitting by adhesive bonding or bolting either FRP or steel plates to RC beams or slabs in bridges and buildings. Compos Part A 2001;32:1345–55. Aiello MA, Ombres L. Cracking and deformability analysis of reinforced concrete beams strengthened with externally bonded carbon fibre reinforced polymer sheets. J Mater Civ Eng 2004;16(5):392–9. Pham H, Al-Mahaidi R. Experimental investigation into flexural retrofitting of reinforced concrete bridge beam using FRP composites. Compos Struct 2004;66(4):617–25. ACI:440-2R-08. Guide for the design and construction of externally bonded FRP systems for strengthening concrete structures. Farmington Hills, Mich., USA: American Concrete Institute; 2008. International Federation of Structural Concrete (fib). Externally bonded FRP reinforcement for RC structures. Technical report bulletin 14. 2001. Japan Society of Civil Engineers. Recommendations for upgrading of concrete structures with use of continuous fibre sheet. Concrete engineering series 41. JSCE; 2001. The Concrete Structure Society. U.K. national structural concrete specification for building construction. 2004. [Camberly, Surrey, UK]. ISIS Canada. An introduction to FRP strengthening of concrete structures. ISIS educational module 4. 2004. IS:456-2000. Code of practice for plain and reinforced concrete. New Delhi: Bureau of Indian Standards; 2000. IS: 455. Portland slag cement-specification (fourth revision). 1989. [Reaffirmed in 1995]. IS: 4031. Indian standard specification methods of physical tests for hydraulic cement: part 11, determination of density. New Delhi: Bureau of Indian Standards; 1988. [Reaffirmed in 2005]. IS: 4031. Indian standard specification methods of physical tests for hydraulic cement: part 2, determination of fineness by specific surface by Blaine Air Permeability method. New Delhi: Bureau of Indian Standards; 1999. [Reaffirmed in 2004]. IS: 4031. Indian standard specification methods of physical tests for hydraulic cement: part 4, determination of consistency of standard cement paste. New Delhi: Bureau of Indian Standards; 1988. [Reaffirmed in 2005]. IS: 4031. Indian standard specification methods of physical tests for hydraulic cement: part 5, determination of initial and final setting times. New Delhi: Bureau of Indian Standards; 1988. [Reaffirmed in 2005]. IS: 4031. Indian standard specification methods of physical tests for hydraulic cement: part 6, determination of compressive strength of hydraulic cement (other than Masonry cement). New Delhi: Bureau of Indian Standards; 1988. [Reaffirmed in 2005]. IS: 2386. Indian standard specification, methods of test for aggregates for concrete: part 1, particle size and shape. New Delhi: Bureau of Indian Standards; 1963. [Reaffirmed in 2002]. IS: 383. Indian standard specification for coarse and fine aggregate from natural sources. New Delhi: Bureau of Indian Standards; 1970. IS: 2386, Indian standard specification, methods of test for aggregates for concrete: part 3, specific gravity, density, voids, absorption and bulking. Bureau of Indian Standards, New Delhi, 1963 [Reaffirmed in 2002]. IS: 2386. Indian standard specification, methods of test for aggregates for concrete: part 4, mechanical properties. New Delhi: Bureau of Indian Standards; 1963. [Reaffirmed in 2002]. IS: 1786. High strength deformed bars and wires for concrete reinforcement — specification. New Delhi: Bureau of Indian Standards; 2008. IS:10262. Concrete mix proportioning- guidelines. New Delhi: Bureau of Indian Standards; 2009. ASTM D 7565-10. Standard test method for determining tensile properties of fibre reinforced polymer matrix composites used for strengthening of civil structures. 2017.